## LCM and HCF

#### LCM and HCF

1. Two numbers are in the ratio 3 : 4. Their L.C.M. is 84. The greater number is

1. Let the numbers be 3p and 4p.
∴ Their LCM = 12p
∴ 12p = 84

 ⇒ p = 84 = 7 12

##### Correct Option: C

Let the numbers be 3p and 4p.
∴ Their LCM = 12p
∴ 12p = 84

 ⇒ p = 84 = 7 12

∴ Larger number = 4p = 4 × 7 = 28

1. Two numbers are in the ratio 3 : 4. If their LCM is 240, the smaller of the two number is

1. Let the number be 3p and 4p. Their LCM = 12p
According to the question,
12p = 240

 ⇒ p = 240 = 20 12

##### Correct Option: C

Let the number be 3p and 4p. Their LCM = 12p
According to the question,
12p = 240

 ⇒ p = 240 = 20 12

∴ Smaller number = 3p = 3 × 20 = 60

1. Three numbers are in the ratio 2 : 3 : 4 and their H.C.F. is 12. The L.C.M. of the numbers is

1. Let the numbers be 2p, 3p and 4p respectively.
∴ HCF = p = 12
∴ Numbers are : 2 × 12 = 24 , 3 × 12 = 36, 4 × 12 = 48
LCM of 24, 36, 48 = 2 × 2 × 2 × 3 × 3 × 2

##### Correct Option: A

Let the numbers be 2p, 3p and 4p respectively.
∴ HCF = p = 12
∴ Numbers are : 2 × 12 = 24 , 3 × 12 = 36, 4 × 12 = 48
LCM of 24, 36, 48 = 2 × 2 × 2 × 3 × 3 × 2 = 144

1. The ratio of two numbers is 4 : 5 and their L.C.M. is 120. The numbers are

1. Suppose the numbers are 4p and 5p respectively
According to question
p × 4 × 5 = 120
⇒ p = 6

##### Correct Option: C

Suppose the numbers are 4p and 5p respectively
According to question
p × 4 × 5 = 120
⇒ p = 6
∴ Required numbers = 4p = 4 × 6 = 24 and = 5p = 5 × 6 = 30

1. If the ratio of two numbers is 2 : 3 and their L.C.M. is 54, then the sum of the two numbers is

1. Let the two numbers are 2p and 3p respectively.
According to question,
LCM = 54
⇒ p ( 3 × 2 ) = 54
⇒ p = 9
Numbers = 2p = 2 × 9 = 18 and, 3p = 3 × 9 = 27

##### Correct Option: C

Let the two numbers are 2p and 3p respectively.
According to question,
LCM = 54
⇒ p ( 3 × 2 ) = 54
⇒ p = 9
Numbers = 2p = 2 × 9 = 18 and, 3p = 3 × 9 = 27
Sum of the two numbers = 18 + 27 = 45