Question

3) Use the Euclidean Algorithm to find
a) GCF(72816, 1684) and use the result to find LCM(72816, 1684).
b) GCF(27644, 46000) and use the result to find LCM(27644, 46000).

Answer 1

Answer:

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Step-by-step explanation:

Solution

Set up a division problem where a is larger than b.

a ÷ b = c with remainder R. Do the division. Then replace a with b, replace b with R and repeat the division. Continue the process until R = 0.

2260 ÷ 816 = 2 R 628 (2260 = 2 × 816 + 628)

816 ÷ 628 = 1 R 188 (816 = 1 × 628 + 188)

628 ÷ 188 = 3 R 64 (628 = 3 × 188 + 64)

188 ÷ 64 = 2 R 60 (188 = 2 × 64 + 60)

64 ÷ 60 = 1 R 4 (64 = 1 × 60 + 4)

60 ÷ 4 = 15 R 0 (60 = 15 × 4 + 0)

When remainder R = 0, the GCF is the divisor, b, in the last equation. GCF = 4

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Answer 2

Answer:

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