Which pairs of numbers have a least common multiple of 12?
a)1 and 3; b)4 and 6; c) 8 and 24; d)24 and 36
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To find the pairs of numbers that have a least common multiple (LCM) of 12, we need to determine the LCM of each pair of numbers and see if it is equal to 12.
a) To find the LCM of 1 and 3, we look for the smallest number that is divisible by both 1 and 3. In this case, the LCM is 3. Since 3 is not equal to 12, the pair (1, 3) does not have a LCM of 12.
b) To find the LCM of 4 and 6, we look for the smallest number that is divisible by both 4 and 6. In this case, the LCM is 12. Since 12 is equal to 12, the pair (4, 6) has a LCM of 12.
c) To find the LCM of 8 and 24, we look for the smallest number that is divisible by both 8 and 24. In this case, the LCM is 24. Since 24 is not equal to 12, the pair (8, 24) does not have a LCM of 12.
d) To find the LCM of 24 and 36, we look for the smallest number that is divisible by both 24 and 36. In this case, the LCM is 72. Since 72 is not equal to 12, the pair (24, 36) does not have a LCM of 12.
Therefore, the only pair of numbers that has a LCM of 12 is (4, 6).