What is the LCM of 10 and 14?

LCM, or Lowest Common Multiple, is the number which is both a multiple of 10 and 14 and is the first number that is.

Many students will look at the two numbers, in this case 10 and 14 and say: "If I multiply 10 and 14, I'll get 140 and that is for sure a multiple of 10 and 14 and so I'll just use that."

And it is true that 140 is a multiple of 10 and 14. But it isn't the lowest. So let's find the lowest.

When I do these, I like to break the numbers in question down to their prime factors:

For 10, the prime factors are 5 and 2 - our LCM will need a 5 and a 2
For 14, the prime factors are 7 and 2 - our LCM will need a 7 and a 2

So we'll need a 2, a 5, and a 7 to make our LCM:

#2xx5xx7=70#

And we can check this by saying:

#10xx7=70#
#14xx5=70#

The first attempt we made, with 140, wasn't the lowest because it had an extra 2 that wasn't needed:

#2xx5xx2xx7=140#

Consider the prime factors of 10 and 14.

#10=2xx5# and #14=2xx7#

Hence the factors of the lowest common multiple must be #2xx5xx7# - Since 2 appears in both it must occur only once in the LCM.

#:. LCM (10, 14) = 2xx5xx7 = 70#

multiples of #10 : 10,20,30,40,50,60,color(red)70, 80 ...#
multiples of #14: 14,28,42,56,color(red)70,84 ......#

Hence, LCM of # 10 and 14 =70#