Solve LCM – HCF

---

Q. If the ratio of two numbers is 5 : 4 and their HCF = 5, find the LCM.

Options: (a) 124 (b) 128 (c) 90 (d) 100

Concept : If two numbers are in ratio a : b, then numbers can be written as: a × HCF and b × HCF

Also, LCM × HCF = Product of two numbers

Solⁿ

Given ratio = 5 : 4
HCF = 5

Numbers = 5×5 and 4×5 (25 and 20)

Now,

LCM = (25 × 20) ÷ 5
LCM = 500 ÷ 5
LCM = 100

Direct Trick : LCM = HCF × (a × b)

So,

LCM = 5 × (5 × 4)
LCM = 5 × 20
LCM = 100

Ans: (d) 100

Tip

• Ratio numbers × HCF = actual numbers


• Use formula: LCM = HCF × (product of ratio terms)

Q.The ratio of two numbers is 3 : 4 and their LCM is 180. What is the bigger number ?

Options: A. 70  B. 40  C. 50   D. 60

Solⁿ

HCF of numbers = LCM​ / Product of ratio terms

Find HCF             

HCF = 180​ / 3 × 4 = 180​/12 = 15

Find the actual numbers :

     First number: 3 × 15 = 45

     Second number: 4 × 15 = 60

Ans: 60

Q.The ratio of two numbers is 5 : 8 and their LCM is 120. What are the two numbers ?

Options: A. 25, 40           B. 20, 32   C. 15, 24     D. 10, 16

Solⁿ

LCM of the numbers = Product of numbers​ / HCF

But an easier rule for ratio:

LCM ÷ (product of ratio terms) = HCF

Find HCF (Common factor)

HCF = 120​/5×8 = 120/40 ​= 3

Find the numbers using ratio

First number = 5×3 = 15

Second number = 8×3 = 24

Ans: 15 and 24

Q. The product of two numbers is 4,235, and their LCM is 385. Find their HCF.
Solⁿ
We know,
Product of two numbers = LCM × HCF

So,
4,235 = 385 × HCF

Therefore,
HCF = 4,235 ÷ 385 = 11

Ans: HCF = 11