Question

What is the value of the positive integer 'n' for which the least common multiple of
36 and 'n' is 500 greater than the greatest divisor of 36 and 'n'.​

Answer 1

Answer:

56

Step-by-step explanation:

The divisors of 36 are 1,2,3,4,6,9,12,18,36

500 more than these are 501,502,503,504,506,509,512,518,536

The LCM of n and 36 must be among these.

All multiples of 36 end with an even digit, so that narrows the LCM of n and 36 down to 502,504,506,512,518,536

504 is the only one of those which is a multiple of 36

So, LCM=504  and GCD= (504-500)=4

GCD×LCM=36×n

4×504=36×n

n=56

i hope this helps you have a good day :)