It is quite clear by studying Matthew 26:17-19, Mark 14:12-16, and Luke 22:7-14 we may conclude that the Last Supper that Jesus ate with his disciples was a Passover meal.

Matthew 26:17-19

17 On the first day of the Feast of Unleavened Bread, the disciples came to Jesus and asked, "Where do you want us to make preparations for you to eat the Passover?" 18 He replied, "Go into the city to a certain man and tell him, 'The Teacher says: My appointed time is near. I am going to celebrate the Passover with my disciples at your house.' " 19 So the disciples did as Jesus had directed them and prepared the Passover.

Mark 14:12-16

12 On the first day of the Feast of Unleavened Bread, when it was customary to sacrifice the Passover lamb, Jesus' disciples asked him, "Where do you want us to go and make preparations for you to eat the Passover?" 13 So he sent two of his disciples, telling them, "Go into the city, and a man carrying a jar of water will meet you. Follow him. 14Say to the owner of the house he enters, 'The Teacher asks: Where is my guest room, where I may eat the Passover with my disciples?' 15He will show you a large upper room, furnished and ready. Make preparations for us there." 16 The disciples left, went into the city and found things just as Jesus had told them. So they prepared the Passover.

Luke 22:7-14

7 Then came the day of Unleavened Bread on which the Passover lamb had to be sacrificed. 8 Jesus sent Peter and John, saying, "Go and make preparations for us to eat the Passover." 9 "Where do you want us to prepare for it?" they asked. 10 He replied, "As you enter the city, a man carrying a jar of water will meet you. Follow him to the house that he enters, 11and say to the owner of the house, 'The Teacher asks: Where is the guest room, where I may eat the Passover with my disciples?' 12He will show you a large upper room, all furnished. Make preparations there." 13 They left and found things just as Jesus had told them. So they prepared the Passover. 14 When the hour came, Jesus and his apostles reclined at the table. 15And he said to them, "I have eagerly desired to eat this Passover with you before I suffer.

However, according to John 18:28, Jesus was arrested and sent to the palace of the Roman governor, Pilate in early morning before the Passover meal. Therefore, it seems that there is an inconsitency between the gospel of John and the synoptic gospels which state that the Passover meal was eaten by Jesus and his disciples the night before his arrest.

John 18:28

28 Then the Jews led Jesus from Caiaphas to the palace of the Roman governor. By now it was early morning, and to avoid ceremonial uncleanness the Jews did not enter the palace; they wanted to be able to eat the Passover. 29 So Pilate came out to them and asked, "What charges are you bringing against this man?"

In order to draw the conclusion that there is an inconsistency in the gospels, we assume that there is a single standard in determining the Passover day. However, there were different calendars for determining the Passover used by different groups and regions during Jesus' time [1]. Therefore, there could be timing difference for Passover depending on what calendar one was using. One scholarly study found that during Jesus' time, the Galileans and Pharisees used the sunrise-to-sunrise standard in reckoning the Passover while the Judeans and Sadducees used the sunset-to-sunset standard in reckoning the Passover [2]. In light of the difference in reckoning, we may conclude that Jesus and his disciples used the Galilean method in reckoning the Passover as recorded in the synoptic gospels while John gospel referred to the Passover based on the Judean method observed by the Judeans and the Sadducees [3]. Both calendars would require slaughter of the Passover lambs on fourteenth day of the month of Nisan i.e. first month of the year mentioned in Exodus 12:2-6.

Exodus 12:2-6

2 "This month is to be for you the first month, the first month of your year. 3 Tell the whole community of Israel that on the tenth day of this month each man is to take a lamb for his family, one for each household. 4 If any household is too small for a whole lamb, they must share one with their nearest neighbor, having taken into account the number of people there are. You are to determine the amount of lamb needed in accordance with what each person will eat. 5 The animals you choose must be year-old males without defect, and you may take them from the sheep or the goats. 6 Take care of them until the fourteenth day of the month, when all the people of the community of Israel must slaughter them at twilight.

The events at the time of Jesus' crucification viewed by the two calendars of Passover according to the study of Harold Hoehner of Dallas Theological Seminary are as follows.

Passover reckoned by Galilean Method (sunrise-to-sunrise):

Nisan 14 began on Thursday sunrise. At about 3 to 5 p.m. Thursday, Passover lambs were slaughtered by people who observed the Galilean method of reckoning of Passover. Jesus and his disciples had their Passover meal which was also the last supper after sunset on Thursday. Jesus was then arrested Thursday night.

Passover reckoned by Judean Method (sunset-to-sunset):

Nisan 14 began on Thursday sunset. Jesus was arrested on Thursday after sunset and the Last Supper with his disciples. On Friday, Passover lambs according to the Judean reckoning were slaughtered at about 3 to 5 p.m. which was now late Nisan 14. This was also the time Jesus died on the cross and was then burried. After sunset on Friday i.e. the night of Nisan 15, the Judeans and Sadducees had their Passover meals.

References:
1. Morgenstern, Hebrew Union College Annual, X, 1-148; Stauffer, p. 95; Finkel, pp. 70-74; M. Black, "The Arrest and Trial of Jesus and the Date of the Last Supper," New Testament Essays, ed. by A. J. B. Giggins (Manchester, 1959), pp. 30-32
2. Julian Morgenstern, "The Calendar of the Book of Jubilees, its Origin and its Character," Vetus Testamentum, V (Janiuary, 1955), 64-65 n. 2;Finegan, pp. 452-453; G. R. Driver, "Two Problems in the New Testament," The Journal of Theological Studies, XVI (October, 1965), 327.
3. Harold W. Hoehner, Chronological Aspecs Of The Life Of Christ, by Zondervan Publishing House, pp. 86-89