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

Question

Nova Allen · Accepted Answer

The answer is #70#.

Finding the multiples of each number in a set and then determining which one is the smallest common multiple will yield the LCM (Lowest Common Multiple) of that 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 process of finding multiples involves multiplying the number you're looking for by each consecutive number. For example, multiples of #3#: #3(3*1), 6(3*2), 9(3*3), 12(3*4), 15(3*5), ...# I hope this is useful.

Genesis Amaya · Answer

#70#

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#

Prime factors are another tool you can use to find this;

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

#LCM = 2 xx 5 xx 7 = 70#

Julian Avila · Answer

undefined The lowest common multiple of 5, 7, and 10 is 70.