Question

Three numbers are in the ratio 4:5:6 and their LCM is 4500. What is their HCF ?​

Answer 1

Let the three numbers be 4a, 5a and 6a.

LCM of 4a, 5a and 6a = 60a

So, 60a = 4500 (given) , i.e, a= 4500/60 = 75

So the numbers are, 4x75=300, 5x75 = 375 and 6x75 = 450

300 = 2 × 2 × 3 × 5 × 5

375 = 3 × 5 × 5 × 5

450 = 2 × 3× 3 × 5× 5

So, HCF =3×5 = 15 Ans.

Answer 2

SOLUTION

GIVEN

• Three numbers are in the ratio 4 : 5 : 6

• Their LCM is 4500

TO DETERMINE

Their HCF

CONCEPT TO BE IMPLEMENTED

HCF :

For the given two or more numbers HCF is the greatest number that divides each of the numbers

LCM :

For the given two or more numbers LCM is the least number which is exactly divisible by each of the given numbers

EVALUATION

Here it is given that three numbers are in the ratio 4 : 5 : 6

Let the numbers are 4x , 5x , 6x

LCM = 60x

So by the given condition

60x = 4500

⇒ x = 75

Hence the required HCF

= x

= 75

FINAL ANSWER

Hence the required HCF = 75

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