Question

how to find out lcm of two unlike fractions ?

what is the lcm of 1/4 and 5/6

Answer 1

Suppose $\frac{a}{b}$ and $\frac{c}{d}$ are two unlike fractions. The following steps show how to find the LCM of $\frac{a}{b}$ and $\frac{c}{d}$ .
1) Find the LCM of b and d = LCM(b,d)
2) Multiply numerator and denominator of first fraction by LCM(b,d)/b.
3) Multiply numerator and denominator of first fraction by LCM(b,d)/d.
4) After this multiplication, denominator of both fractions are same.
5) Find LCM of new numerators.
The answer is LCM(numerators)/LCM(b,d)

Now lets find the LCM of 1/4 and 5/6.
1) Find the LCM of 4 and 6 = 12
2) Multiply first fraction by $\frac{12}{4}$ = 3
Multiply the second fraction by $\frac{12}{6}$ = 2
So now first fraction is $\frac{1\times 3}{4\times 3}=\frac{3}{12}$
and the second fraction is $\frac{5\times 2}{6\times 2}=\frac{10}{12}$
3) Since both denominators are same, LCM of numerators 3 and 10 = 30
4) Hence LCM of $\frac{1}{4}$ and $\frac{5}{6}$ is $\frac{30}{12}$
After simplification $\frac{30}{12}$ = $\frac{5}{2}$
Therefore, LCM of 1/4 and 5/6 is $\frac{5}{2}$.