LCM of 3/4 , 6/7 , 7/8 is (1) 3 + 6 + 9 (2) 9 (3) 42 (4) 7

Question

LCM of \(\frac {3}{4} , \frac {6}{7} , \frac {7}{8}\) is

(1) 3 + 6 + 9

(2) 9

(3) 42

(4) 7

Answer 1

Correct option is (3) 42

As we know that,

\(LCM = \frac {\text {LCM of numerator}}{\text {HCF of Denominator}}\)

Numerators of the fractions = 3, 6, 7

Prime factors of 3 = 1 x 3

Prime factors of 6 = 1 x 2 x 3

Prime factors of 7 = 1 x 7

\(\therefore\) LCM of 3, 6 and 7 = 2 x 3 x 7 = 42.

Denominators of the fractions = 4, 7, 8

Factor of 4 = 1, 2 and 4

Factor of 7 = 1 and 7

Factor of 8 = 1, 2, 4 and 8

\(\therefore\) HCF of 4, 7 and 8 = 1

Now, LCM of \(\frac {3}{4}, \frac {6}{7}\) and \(\frac {7}{8}\) is \(\frac {42}{1}.\)