Question

Find the L.C.M of 3/4,6/7,9/8.

Answer 1

Q. Find the L.C.M of 3/4, 6/7, 9/8.
Ans.
The rule of finding the L.C.M of fractions is = L.C.M of Numerators/H.C.F of Denominators.

So, here the Numerators are 3, 6, 9.
The L.C.M. of 3, 6, 9 is 18.
Now the Denominators are 4, 7, 8.
The H.C.F of 4, 7, 8 is 1.

So, the L.C.M of 3/4, 6/7, 9/8 is 18/1= 18. (Ans.)

I try my best to give the answer briefly. But I think it is not enough to express. So, I have done this math in my copy fully and I send the picture as an attachment.

Answer 2

$\bf LCM \: of \: \left( \frac{3}{4}, \frac{6}{7}, \: \frac{9}{8} \right) = 18$

Given:

• $\frac{3}{4}, \: \frac{6}{7}, \: \frac{9}{8}$

To find:

• LCM of given rational numbers.

Solution:

Concept to be used:

$\bf LCM \left( \frac{a}{b}, \: \frac{c}{d}, \: \frac{e}{f}\right) = \frac{LCM(a, \: c ,\: e)}{HCF(b, \: d, \: f)}$

Step 1:

Find the LCM of the numerators.

Do Prime factor of 3, 6 and 9.

$3 = 3 \times 1$

$6 = 3 \times 2$

$9 = 3 \times 3$

$LCM(3,6,9) = {3}^{2} \times 2$

$LCM(3,6,9) = 9 \times 2$

$\bf LCM(3,6,9) = 18$

Step 2:

Find the HCF of the denominator.

Do prime factors of 4,7, and 8.

$4 = 2 \times 2 \times 1$

$7 = 7 \times 1$

$8 = 2 \times 2 \times 2 \times 1$

It is clear that, only '1' is common in prime factors.

$\bf HCF (4,7,8) = 1$

So,

$LCM \: of \: \left( \frac{3}{4} , \frac{6}{7} , \: \frac{9}{8} \right) = \frac{LCM(3, \: 6 ,\: 9)}{HCF(4, \: 7, \: 8)}$

$LCM \: of \: \left( \frac{3}{4} , \frac{6}{7} , \: \frac{9}{8} \right) = \frac{18}{1}$

Thus,

$\bf LCM \: of \: \left( \frac{3}{4}, \frac{6}{7} , \: \frac{9}{8} \right) = 18$

Learn more:

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