GCD times LCM equals the product
For two numbers, GCD x LCM = the product of the numbers. Once you know one, divide to get the other. Example: GCD(84, 120) = 12, so LCM = 84 x 120 / 12 = 840.
Find the GCD by subtracting or dividing
The GCD of two numbers also divides their difference. Keep replacing the larger number with the remainder until one divides the other. Example: GCD(84, 120): 120 - 84 = 36, then 84 - 2 x 36 = 12, and 12 divides 36. GCD = 12.
Use prime factors for bigger numbers
Write each number as primes. The GCD takes the smaller power of each shared prime; the LCM takes the larger power of every prime. Example: 72 = 2^3 x 3^2 and 60 = 2^2 x 3 x 5. GCD = 2^2 x 3 = 12. LCM = 2^3 x 3^2 x 5 = 360.
Practice problems
- LCM(48, 36)
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GCD(48, 36) = 12, so LCM = 48 x 36 / 12 = 144.
- LCM(15, 28)
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GCD(15, 28) = 1 because they share no factors, so LCM = 15 x 28 = 420.
- GCD(84, 120)
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120 - 84 = 36, then 84 - 2 x 36 = 12. GCD = 12.
References
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