Question

56. exercise. for natural numbers a and b, give a suitable definition for "least common multiple of a and b", denoted lcm(a, b). construct and compute some examples.

Answer 1

LCM(a, b) ≡ a×b/GCD(a, b)

LCM(6, 9) = 6*9/3 = 18 . . . . . . . (2 [ 3 ) 3] = 18 . . . ( ) product = 6; [ ] product = 9

LCM(2,5) = 2*5/1 = 10 . . . . . . . . (2 [ 1 ) 5 ] = 10

LCM(27, 45) = 27*45/9 = 135 . . (3 [ 9 ) 5] = 135

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In the above LCM products, the number in [ ) brackets is the GCD.