15) If the LCM and GCD of 24 and an unknown number are 72 and 12 respectively then find the unknown number
Answers
Answer:
Q:If HCF (72,120)=24,then find LCM(72,120)
= LCM = 72*120 / HCF = 8640 / 24 = 360. Therefore, LCM of 72 120 = 360.
Answer:
Are the GCD, LCM of two numbers 12 and 72 if one number is 24, what is the second number?
So, the main fact this question wants you to know is that for two numbers a and b, GCD(a,b) * LCM(a,b) = a*b. In this case, GCD*LCM = 864 = 24 * b, where b is the unknown second number. Divide both sides by 24, and you get b = 36. So far, so good: we get an integer as the second number. Now we need to check to make sure the GCD and LCM of 24 and 36 are 12 and 72, respectively.
What is the GCD of 24 and 36? Well, 24 = 2*2*2*3, and 36 = 2*2*3*3, so the prime factors common to both are two 2’s and a 3, thus the GCD is 2*2*3 = 12. So that checks out (24 = 2*12, 36 = 3*12)
The LCM of 24 and 36 can be found by trying out a few of the lowest multiples of each: multiples of 24 are 24, 48, 72, 96, 120, 144, …, while multiples of 36 are 36, 72, 108, 144, … - the lowest multiple in common is 72, so that checks out.
So the other number you’re looking for is 36.