Question

Find two digit number whose HCF is 24 and LCM is 144

Answer 1

Given :

L.C.M= 144

H.C.F. = 24

Let the two numbers be p & q

L.C.M × H.C.F = Product of the two numbers

L.C.M = Product of the two numbers/ H.C.F

L.C.M. = (p×q)/H.C.F.


144 = pq /24

pq= 144× 24

pq= (2×2×2×2×3×3)× (2×2×2×3)

pq= (2⁴×3²)×(2³×3¹)

pq= (2⁴× 2³)× (3²×3¹)

pq= 2⁷ × 3³

pq = 3456

H.C.F. (pq) = 24 = 2³ × 3¹

L.C.M. depends on pq & H.C.F.

L.C.M = pq & H.C.F= 3456 & 24

We can say that (p,q) = (24, 144) ; (48, 72) ; (72, 48) ; (144. 24)

Hence, the two digit numbers are= 24 or, 48 or 72 whose L.C.M = 144 & H.C.F = 24

==================================================================
Hope this will help you....

Answer 2

Solution :-

Let the two numbers be a and b

We know that LCM*HCF = Product of the two numbers

LCM is 144 and HCF is 24

⇒ 144*24 = a*b

LCM (ab) = ab/HCF

144 = ab/24

ab = (24*144)

ab = 3456

3456 = 2⁷ × 3³

Since HCF (ab) = 24 = 2³ × 3

And, since LCM depends on ab and HCF and we have ab and HCF as 3456 and 24 respectively.

So, we can say that (ab) = (144, 24) ; (48, 72) ; (72, 48) and (24, 144)

So, one of the required two numbers 24 or 48 or 72 whose LCM is 144 and HCF 24 respectively.

Answer.