Question

Using the fact that g.c.d(a, b) L.c.m.(a, b) = ab, find L.c.m..(115, 25)

Answer 1

Given : g.c.d(a, b) L.c.m.(a, b) = ab,  

To find : L.c.m..(115, 25)

Solution:

a = 115

b = 25

g.c.d(a, b) L.c.m.(a, b) = ab

=> L.c.m.(a, b) = ab / g.c.d(a, b)

a = 115

b = 25

g.c.d(115, 25)

115 = 25 * 4 +  15

25 = 15 * 1 + 10

15 = 10 * 1 + 5

10 = 5 * 2

g.c.d(115, 25) = 5

L.c.m.(115, 25) = 115 * 25 / 5

=>  L.c.m.(115, 25) = 115 * 5

=>   L.c.m.(115, 25) = 575

L.c.m.(115, 25) = 575  

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Answer 2

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