## LCM and HCF

#### LCM and HCF

1. The product of HCF and LCM of 18 and 15 is

1. HCF of 18 and 15
18 = 2 x 3 x 3
15 = 3 x 15 = 3
LCM of 18 and 15 = 2 x 3 x 3 x 5 = 90
∴ Product of HCF and LCM of both numbers = 3 x 90 = 270

##### Correct Option: D

HCF of 18 and 15
18 = 2 x 3 x 3
15 = 3 x 15 = 3
LCM of 18 and 15 = 2 x 3 x 3 x 5 = 90
∴ Product of HCF and LCM of both numbers = 3 x 90 = 270

1. The HCF of two numbers is 15 and their LCM is 225. If one of the numbers is 75, then find the another number.

1. Product of LCM and HCF = Product of two numbers

##### Correct Option: D

Let the other number = N
Product of LCM and HCF = Product of two numbers
Then, N x 75 = 15 x 225
∴ N = (15 x 225)/75 = 45

1. The HCF of three numbers is 23. If they are in the ratio of 1 : 2 : 3, then find the numbers ?

1. Let the numbers are N, 2N and 3N.
Where, N = HCF

##### Correct Option: B

Let the numbers are N, 2N and 3N.
Where, N = HCF
Given that, N = 23
∴ The numbers are 23, 46 and 69.

1. The HCF and LCM of two numbers m and n are respectively 6 and 210. If m + n = 72, then 1/m + 1/n is equal to

1. We have, m x n = 6 x 210 = 1260
∴ 1/m + 1/n

##### Correct Option: D

We have, m x n = 6 x 210 = 1260
∴ 1/m + 1/n = (m + n)/mn = 72/1260 = 4/70 = 2/35

1. The ratio of two numbers is 5 : 6 and their LCM is 480, then their HCF is

1. Let numbers are 5N and 6N.
Now, HCF of these two numbers is N.

We know that,
LCM x HCF = Product of two numbers

##### Correct Option: B

Let numbers are 5N and 6N.
Now, HCF of these two numbers is N.

We know that,
LCM x HCF = Product of two numbers
⇒ 480 x N = 5N x 6N
⇒ 480N = 30N2
⇒ N =16