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

View Hint View Answer Discuss in Forum
Let the numbers be 4p and 5p.
∴ H.C.F. = p = 8
∴ Numbers = 4p = 4 × 8 = 32 and 5p = 5 × 8 = 40Correct 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
 The LCM of two numbers is 48. The numbers are in the ratio 2 : 3. The sum of the numbers is

View Hint View Answer Discuss in Forum
If the numbers be 2p and 3p , then LCM = 6p
∴ 6p = 48 ⇒ p = 8
∴ Required sum = 2p + 3p = 5pCorrect Option: C
If the numbers be 2p and 3p , then LCM = 6p
∴ 6p = 48 ⇒ p = 8
∴ Required sum = 2p + 3p = 5p = 5 × 8 = 40
 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

View Hint View Answer Discuss in Forum
Let the numbers be 3p and 4p respectively
As we know that ,
First number × second number = HCF × LCM
⇒ 3p × 4p = 2028⇒ p^{2} = 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⇒ p^{2} = 2028 = 169 3 × 4
∴ p = √169 = 13
∴ Sum of the numbers = 3p + 4p = 7p = 7 × 13 = 91
 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 :

View Hint View Answer Discuss in Forum
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
 Two numbers are in the ratio 3 : 4. If their HCF is 4, then their LCM is

View Hint View Answer Discuss in Forum
Numbers = 3p and 4p
HCF = p = 4
∴ LCM = 12p = 12 × 4Correct Option: A
Numbers = 3p and 4p
HCF = p = 4
∴ LCM = 12p = 12 × 4 = 48