Question: ↑
Answer:
Solution:
The GCD of a, b is the largest positive number that divides both a and b without a remainder
Prime factorization of 20: 2 · 2 · 5
20
20 divides by 2 20 = 10 · 2
= 2 · 10
10 divides by 2 10 = 5 · 2
= 2 · 2 · 5
2, 5 are all prime numbers, therefore no further factorization is possible
= 2 · 2 · 5
Prime factorization of 30: 2 · 3 · 5
30
30 divides by 2 30 = 5 · 2
= 2 · 15
15 divides by 3 15 = 5 · 3
= 2 · 3 · 5
2, 3, 5 are all prime numbers, therefore no further factorization is possible
= 2 · 3 · 5
The prime factors common to 20, 30 are
= 2 · 5
Multiply the numbers: 2 · 5 = 10
Answer: 10
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Least Common Multiplier (LCM)
The LCM of a, b is the smallest positive number that is divisible by both a and b
Prime factorization of 20: 2 · 2 · 5
20
20 divides by 2 20 = 10 · 2
= 2 · 10
10 divides by 2 10 = 5 · 2
= 2 · 2 · 5
2,5 are all prime numbers, therefore no further factorization is possible
= 2 · 2 · 5
Prime factorization of 30: 2 · 3 · 5
30
30 divides by 2 30 = 15 · 2
= 2 · 15
15 divides by 3 15 = 5 · 3
= 2 · 3 · 5
2, 3, 5 are all prime numbers, therefore no further factorization is possible
= 2 · 3 · 5
Multiply each factor the greatest number of times it occurs in either 20 or 30
= 2 · 2 · 5 · 3
Multiply the numbers: 2 · 2 · 5 · 3 = 60
Answer: 60
