What is the lowest common multiple of #5, 7 and 10#?

To find the LCM (Lowest common multiple) of a set of numbers, you first find the multiples of each number and then identify the smallest common one among the set.

In this case, using #5#, #7#, and #10#. The smallest common multiple of each would be #70#. If we find the multiples of each of the numbers, we can see that no other number before #70# is common to all of them.

Multiples of #5#: #" "5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, ...#

Multiples of #7#: #" "7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, ...#

Multiples of #10#: #" "10, 20, 30, 40, 50, 60, 70, 80, ...#

If you realize, the only common multiple up to this point is #70#. There may be other common multiples but you are looking for the smallest (or lowest) one.

Note: The way you find multiples is to multiply the number you are trying to find numbers for by each number in succession.

For example, multiples of #3#: #3(3*1), 6(3*2), 9(3*3), 12(3*4), 15(3*5), ...#

Hope this helps!!

You do not need to consider #5# at all the calculation, because it is a factor of #10#. So any number divisible by #10# will automatically be divisible by #5# as well.

#7 and 10# do not have any common factors (other than #1#), so their LCM will be their product.

#:. LCM = 7 xx10 = 70#

You can use prime factors to find this as well;

#" "5 = color(white)(www) 5#
#" "7 =color(white)(wwwww) 7#
#" "10 = ul(2 xx 5color(white)(www))#

#LCM = 2 xx 5 xx 7 = 70#