## LCM and HCF

#### LCM and HCF

1. The ratio of two numbers is 4 : 5 and their H.C.F. is 8. Then their L.C.M. is

1. Let the numbers be 4p and 5p.
∴ H.C.F. = p = 8
∴ Numbers = 4p = 4 × 8 = 32 and 5p = 5 × 8 = 40

##### Correct Option: D

Let the numbers be 4p and 5p.
∴ H.C.F. = p = 8
∴ Numbers = 4p = 4 × 8 = 32 and 5p = 5 × 8 = 40
∴ Their LCM = 160

1. The LCM of two numbers is 48. The numbers are in the ratio 2 : 3. The sum of the numbers is

1. If the numbers be 2p and 3p , then LCM = 6p
∴ 6p = 48 ⇒ p = 8
∴ Required sum = 2p + 3p = 5p

##### Correct Option: C

If the numbers be 2p and 3p , then LCM = 6p
∴ 6p = 48 ⇒ p = 8
∴ Required sum = 2p + 3p = 5p = 5 × 8 = 40

1. Two numbers are in the ratio 3 : 4. The product of their H.C.F. and L.C.M. is 2028. The sum of the numbers is

1. Let the numbers be 3p and 4p respectively
As we know that ,
First number × second number = HCF × LCM
⇒ 3p × 4p = 2028

 ⇒ p2 = 2028 = 169 3 × 4

∴ p = √169 = 13

##### Correct Option: D

Let the numbers be 3p and 4p respectively
As we know that ,
First number × second number = HCF × LCM
⇒ 3p × 4p = 2028

 ⇒ p2 = 2028 = 169 3 × 4

∴ p = √169 = 13
∴ Sum of the numbers = 3p + 4p = 7p = 7 × 13 = 91

1. The ratio of the sum to the LCM of two natural numbers is 7 : 12. If their HCF is 4, then the smaller number is :

1. Let the numbers be 4p and 4q where p and q are prime to each other.
LCM = 4pq

 ∴ ( 4p + 4q ) = 7 4pq 12

⇒ 12 (p + q) = 7pq
⇒ p = 3, q = 4

##### Correct Option: C

Let the numbers be 4p and 4q where p and q are prime to each other.
LCM = 4pq

 ∴ ( 4p + 4q ) = 7 4pq 12

⇒ 12 (p + q) = 7pq
⇒ p = 3, q = 4
∴ Smaller number = 4 × 3 = 12

1. Two numbers are in the ratio 3 : 4. If their HCF is 4, then their LCM is

1. Numbers = 3p and 4p
HCF = p = 4
∴ LCM = 12p = 12 × 4

##### Correct Option: A

Numbers = 3p and 4p
HCF = p = 4
∴ LCM = 12p = 12 × 4 = 48