## LCM and HCF

#### LCM and HCF

1. Find the least number which when divided by 12, 15, 20 and 24 leaves the same remainder 2 in each case ?

1. Required number = LCM of (12, 15, 20, 24) + 2

##### Correct Option: A

Required number = LCM of (12, 15, 20, 24) + 2
= 120 + 2 = 122

1. If there number are 2a, 5a, and 7a, what will be their LCM?

1. Required LCM = a x 2 x 5 x 7

##### Correct Option: A

Required LCM = a x 2 x 5 x 7 = 70a

1. What will be the HCF of ( 2 x 3 x 7 x 9 ), ( 2 x 3 x 9 x 11 ) and ( 2 x 3 x 4 x 5 )?

1. ∴ Required HCF = Product of common prime factors having least powers

##### Correct Option: C

Given factors
2 x 3 x 7 x 9; 2 x 3 x 9 x 11; 2 x 3 x 4 x 5
∴ Required HCF = Product of common prime factors having least powers = 2 x 3

1. Find the LCM of 1/3, 2/9, 5/6 and 4/27.

1. LCM of fractions = (LCM of numerators) / (HCF of denominators)

##### Correct Option: C

We known that,
LCM of fractions = (LCM of numerators) / (HCF of denominators)

∴ Required LCM = (LCM of 1, 2, 5, and 4) / (HCF of 3, 9, 6 and 27)
∴ = 20/3

1. Find the LCM of 2/3, 3/5, 4/7 and 9/13.

1. Required LCM = (LCM of 2, 3, 4, 9) / (HCF of 3, 5, 7, 13)

##### Correct Option: A

Required LCM = (LCM of 2, 3, 4, 9) / (HCF of 3, 5, 7, 13)
= (4 x 9)/1
= 36