as their L.C.M.?
The L.C.M and H.C.F. of two numbers are 2443 and 12 respective
difference between them is 60; find such pair of numbers. Find a
by inspection trace the required pair out of them)
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Answer:
An LCM is a multiple of the HCF.
So if the LCM and HCF of two numbers are 2448 and 12, the LCM = 12*204.
The two numbers are x and (x+60).
The product of HCF and LCM = product of the two numbers, or
12*2448 = x(x+60)
x^2+60x = 29376
x^2+60x-29376=0
x1 = [-60+(3600+117504)^0.5]/2
= [-60+121104^0.5]/2
= [-60+348]/2
= 288/2
= 144
x2 = [-60–348]/2 = -204
The numbers are 144 and 204 or -204 and -144.
Check; Factors of 144 = 2x2x2x2x3x3
204 = 2x2x3x17
HCF = 2x2x3 = 12
LCM = 2^4x3^2x17 = 2448. Correct.
Step-by-step explanation:
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