Question

Find​ a) the greatest common divisor​ (GCD) and​ b) the least common multiple​ (LCM).

40

and 900

Answer 1

Answers: GCD = 20 and LCM = 1800

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Step-by-step explanation:

Let's write the prime factorization for each value given to us.

• 40 = 4*10 = (2*2)*(2*5) = 2*2*2*5
• 900 = 90*10 = (3*3*2*5)*(2*5) = 2*2*3*3*5*5

In short,

• 40 = 2*2*2*5
• 900 = 2*2*3*3*5*5

Compare the prime factors to see that "2*2" is common among both, and each shares a common "5" as well.

Therefore 2*2*5 = 4*5 = 20 is the GCD. Factor trees could help visualize what's going on.

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To get the LCM, we multiply the given values and then divide by the GCD. This applies only when we have two values. If there are more than two values, then you'll need to do a slightly different method.

LCM = (x*y)/(GCD)

LCM = (40*900)/(20)

LCM = 1800

Use of a spreadsheet can help verify we have the correct LCM.