LCM of two number is 12 time Thier HCF sum of LCM & HCF is 403 if one number is 93 find the other number?
Answers
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Step-by-step explanation:
The LCM of two numbers is 12 times their HCF. The sum of HCF and LCM is 403. If one number is 93, then find the other number?
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Here is how I solved this in mind without using formulas or pen/paper
Factors of 93 => 31 and 3
Unlikely that 3 will be the HCF as 12*3 is 36 which can’t be the LCM for 93.
If 31 is the HCF, which is a prime number, the other number must be a multiple of 31 and 4 as the LCM is a multiple of 4 (It’s 12 times the HCF)
So the other number could be 31 * 4 => 124
Verify that the LCM (HCF*12 = 21*12 = 372) is a multiple of 124
Verify by doing the sum of HCF (31) and LCM (372) = 403 as per the statement
Hence the answer is 124
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If the lcm is 12 time the hcf
Lcm=12*hcf
Lcm+hcf= 403
12*hcf +hcf=403
On solving
hcf=31
Means lcm=372
Now lcm*hcf=product of the no.
Let the no. To be found is x
Means 372*31=93*x
On solving for x
We get x=124
So the other no. Is 124
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