Q. 43.7( 3 Votes )

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

Answer :

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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