LCM, HCF and GCD Practice
Practice problems on least common multiple, highest common factor, and greatest common divisor including calculations and word problems
Questions
Which of the following sets of the numbers will have the highest common factor equal to 18?
- 38, 58, 124
- 36, 54, 126
- 28, 54, 126
- 36, 54, 128
Which of the following sets of the numbers will have the LCM equal to 72?
- 14, 12, 18
- 16, 12, 14
- 12, 18, 24
- 18, 24, 28
Find the LCM of (a + b)2 and (a + b).
- (a + b)
- (a + b)2
- (a + b)3
- a - b
Which of the following sets of numbers will have LCM equal to 300?
- 85 and 90
- 75 and 60
- 60 and 95
- 76 and 62
What is the LCM of pq (p - q) and pqr (p - q)?
- (p - q)
- pqr
- pqr(p - q)
- pq(p - q)
What is the LCM of x2 - z2 and x + z?
- (x + z) (x - z)
- (x + z)2
- (x - z)2
- x - z
Which of the following sets of numbers will have the LCM equal to 105?
- 15 and 27
- 27 and 61
- 21 and 35
- 15 and 21
Which of the following sets of numbers will have LCM equal to 672?
- 84 and 32
- 89 and 35
- 84 and 36
- 94 and 32
Which of the following numbers has the least common multiple as 112?
- 16, 18
- 14, 16
- 12, 14
- 16, 20
What is the least common multiple of p3 + q3 + 3p2q + 3pq2 and p2 - q2?
- (p + q)3
- p + q
- (p + q)3 (p - q)
- (p - q)3 p + q
Which of the following sets of numbers will have 84 as LCM?
- 26, 24, 18
- 28, 14, 21
- 18, 34, 21
- 28, 34, 16
Which of the following sets of numbers will have 80y2x as LCM?
- 4y2, 16x, 8y
- 2y2, 16xy, 8a
- 8y2, 16xy, 10y
- 18y2, 16xy, 4y
Which of the following sets of numbers have 140ab as LCM?
- 10ab, 20ab, 28ab
- 11ab, 21ab, 28ab
- 12ab, 20ab, 14ab
- 20ab, 26ab, 14ab
Alex and her three friends go for lunch and find a deal on packages of 6 tacos. He wants to buy the minimum number of packages. So, each gets the same number of tacos and none are left over. How many packages must he buy?
- 11
- 12
- 13
- 14
Alex can make groups of 3, 4 and 9 pencils with no left over. What is smallest number of pencils Alex needs to make these groups?
- 28
- 30
- 34
- 36
During summer months, one ice cream truck visits Williams neighbourhood every 4 days and another ice cream truck visits her neighbourhood every 5 days. If both the trucks visited today, when is the next time when both the trucks will visit on the same day?
- After 20 days
- After 28 days
- After 30 days
- After 36 days
Which of the following sets of numbers will have 560b4a as LCM?
- 28b, 20ab3, 16b4
- 28b, 20ab2, 16b4
- 20b2, 28ab, 18b4
- 28b4, 18ab3, 16b
Sam has two pieces of cloth. One piece is 72 inches wide and the other piece is 90 inches wide. She wants to cut both pieces into strips of equal width that are as wide as possible. How would she cut the strips?
- She should cut each piece to be 14 inches wide.
- She should cut each piece to be 16 inches wide.
- She should cut each piece to be 18 inches wide.
- She should cut each piece to be 20 inches wide.
One trip around a running track is 440 yards. One jogger can complete one lap in 8 minutes, the other can complete it in 6 minutes. How long will it take for both joggers to arrive at their starting point together if they start at the same time and maintain their jogging pace?
- 12 minutes
- 16 minutes
- 20 minutes
- 24 minutes
Dan exercise every 12 days and Kevin every 8 days. Dan and Kevin both exercised today. How many days will it be until they exercise together again?
- They will exercise on the same day after every 24 days.
- They will exercise on the same day after every 28 days.
- They will exercise on the same day after every 32 days.
- They will exercise on the same day after every 40 days.
Rosa is making a game board that is 55 inches by 75 inches. She wants to use square tiles. What is the size of the largest tile she can use?
- 4 inches
- 5 inches
- 7 inches
- 10 inches
What is the LCM of 22, 54 and 108?
- 5442
- 2926
- 1188
- 428
The bikers are riding on a circular path. The first rider completes a round in 35 minutes. The second biker complete a round in 25 minutes. If they both started at the same place and time and go in the same direction, after how many minutes will they meet again at the starting point?
- 155
- 165
- 175
- 180
Cameron is making bead necklace. He has 90 green beads and 108 blue beads. What is the greatest number of identical necklaces he can make if he wants to use all of the beads?
- 16
- 18
- 26
- 28
Sharon plants 40 apple trees and 10 peach trees. She wants the same number and type of trees per row. What is the maximum number of trees she can plant per row?
- 20
- 10
- 8
- 4