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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.

Factors 12 18 72
2 6 (12/2) 9 (18/2) 36 (72/2)
3 2 (6/3) 3 (9/3) 12 (36/3)

In the illustration above 12, 18 and 72 is the group of numbers.

  • When the common factor of 2 is taken into account the remaining values are 6, 9 and 36.
  • With the next common factor of 3 the results become 2, 3 and 12.

Since there are no more common factors between 2, 3 and 12 the HCF would be : 2x3=6.

In other words, HCF is that number that is contained in each member of a group. The HCF is the multiple of all prime factors that 12, 18 and 72 share. This is how the HCF is determined.

Now that you know the method here is the easy part.


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