Question

Use the Euclidean algorithm to calculate the greatest common divisor of 2, 354 and 6, 655.
Hence, find the least common multiple of 2, 354 and 6, 655.

Answer 1

The least common multiple of 2354 and 6655 calculated using the Euclidean algorithm is 142170.

• The Euclidean algorithm is used to obtain the greatest common factor of two numbers by repetitive division until a remainder of 0 is obtained

• The value of the greatest common factor obtained is then used to divide the product of the two values to obtain their lowest common multiple.

The calculation to obtain the Greatest Common Factor is performed as follows :

6655 / 2354 = 2 R 1947

2354 / 1947 = 1 R 407

1947 / 407 = 4 R 319

407 / 319 = 1 R 88

319 / 88 = 3 R 55

88 / 55 = 1 R 33

55 R 33 = 1 R 22

33 R 22 = 1 R 11

22 R 11 = 2 R 0

Therefore, the greatest common divisor of 6655 and 2354 is 11

The Least Common Multiple is the product of the two numbers divided by the greatest common factor :

• (6655 × 2354) ÷ 11
• 15665870 ÷ 11 = 142170

Therefore, the least common multiple of 6655 and 2354 is 142170.

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