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12 May 2022 LCM & HCF

LCM of two numbers is 60 times their HCF. If sum of LCM and HCF is 549. If one number is 45, then other number is

OPtion

1) 96
2) 132
3) 181
4) 162
5) 180
6) 126
7) 108
8) 216
9) 144
10) None of these

Solution

Given, one number=45 and LCM=60HCF. Let other number=x
We know, product of LCM & HCF = Product of two numbers
LCM*HCF = 45x
60HCF*HCF = 56x ----(i)
Also, LCM + HCF = 549
60HCF + HCF = 549
61HCF = 549
⇒ HCF=9
Now substituting HCF=9 in Eqn (i), we get 60*9*9 = 45x
⇒ x=108

Correct Option: 7 Best Solution (3)

G.S.Kantharao   2 years AGO

Let H.C.F =H
L.C.M =60H
L.C.M+H.C.F=60H+H=549
H=549/61=9
L.C.M=60*9=540
Other Number=540*9/45=108
My option is 7👈

Like? Yes (4) | No   

Dr.Dipin Singh   2 years AGO

If hcf is x, then
x+60x=549
x=9=hcf
Lcm=60x=540
One number is given as 45,
Hence other number =9*540/45= 108

Like? Yes (1) | No   

RAMADURAI NATESAN   2 years AGO

Let Nos. be M and N. M = 45.
L = 60H. L + H = 549 = 61 H. H = 9.L = 540.
M*N = L*H =4860. N = 4860/45 =108

Like? Yes (1) | No