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

Here, 115 > 25

115 = 25 × 4 + 15

25 = 15 × 1 + 10

15 = 10 × 1 + 5

10 = 5 × 2 + 0

The last non- zero remainder is 5.

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

Now, by Euclid’s Algorithm

g. c. d(a, b) × l.c.m.(a, b) = ab

Here, a = 115, b = 25

g. c. d(115, 25) × l.c.m.(115, 25) = 115 × 25

5 × l.c.m.(115, 25) = 115 × 25

l.c.m.(115, 25) =

l.c.m.(115, 25) = 115 × 5

Therefore, l.c.m.(115, 25) = 575

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