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LCM / HCF

Calculate the lowest common multiple (lcm) and the highest common factor (hcf) of a group of numbers of any length.
LCM

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.

HCF
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.

common factor 12 18 72
2 6 (12/2) 9 (18/2) 36 (72/2)
3 2 (6/3) 3 (9/3) 12 (36/3)

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.


HCF / LCM
Input the numbers - separate each number with a space




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