What is the L.C.M. of $$\frac{10}{21},\frac{20}{63},\frac{55}{56}$$ ?

LCM of a fraction = $$\dfrac{\text{LCM of Numerator}}{\text{HCF of denominator}}$$

L.C.M. of $$\dfrac{10}{21},\dfrac{20}{63},\dfrac{55}{56}$$:

Prime factors of 10 are 5 and 2
Prime factors of 20 are 5, 2 and 2
Prime factors of 55 are 5 and 11
Therefore, LCM of 10, 20 and 55 = $$5\times2\times2\times11 = 220$$
Prime factors of 21 = 7 and 3
Prime factors of 63 = 7, 3 and 3
Prime factors of 56 = 7, 2, 2, 2
Therefore, HCF of 21, 63 and 56 = 7.

Therefore, L.C.M. of $$\dfrac{10}{21},\dfrac{20}{63},\dfrac{55}{56} = \dfrac{220}{7}$$