LCM / HCF
Calculate the lowest common multiple (lcm) and the highest common factor (hcf) of a group of numbers of any length.
The lowest common multiple (lcm) of a group of numbers is the smallest number (not zero) that is a multiple of all the numbers in the group.
For example, to find the LCM of 6, 18, 28 list the prime factors of each number.
6: 2 x 3
18: 2 x 3 x 3
28: 2 x 2 x 7
Multiply each factor the greatest number of times it occurs in any of the numbers. 6 has one 2 and one 3; 18 has one 2 and two 3s, and 28 has two 2s and one 7.
We multiply 2 two times; 3 two times; and 7 once. This gives us 252, the smallest number that can be divided evenly by 6, 18, and 28.
The highest common factor (HCF) of a group of numbers is the highest number that is divisible by all the numbers, without a remainder. It is the highest value that is common to all the numbers of the group.
For example, 6 is the greatest number that will divide into 12, 18 and 72 without a remainder.