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16 votes
16 votes
Find the least common multiple of 8y^2 and 7m

User Zakhar
by
2.7k points

1 Answer

14 votes
14 votes

Answer:
56y^2m

which is the same as writing 56y^2m

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Step-by-step explanation:

Let's focus on the coefficients 8 and 7 for now.

To find the LCM of those values, list out the multiples. Circle the smallest number that can be found in both sets at the same time.

  • multiples of 8 are: 8, 16, 24, 32, 40, 48, 56, 64, ...
  • multiples of 7 are: 7, 14, 21, 28, 35, 42, 49, 56, 63, ....

We see that 56 is the LCM of 7 and 8.

Or you could use this shortcut

LCM = (x*y)/GCF

where x and y are the two numbers. The mention of "GCF" refers to the GCF of x and y. In this case, the GCF is 1 so,

LCM = (x*y)/GCF = (8*7)/1 = 8*7 = 56.

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Once we determine that, we look at the variable terms now.

The y^2 and m will be tacked onto the 56 to arrive at the final answer 56y^2m

This is because y and m are the unique variables, and we go for the highest exponent of each. It's similar to the LCM formula used earlier.

User LogicalAnt
by
2.9k points