Question

Find the least number which when decreased by 9, is divisible by 18, 24. 30 and 36.​

Answer 1

Answer:

First, find the lowest common multiple of the 4 given numbers.

Then add 9.

Find the LCM by using prime factors.

36=(2^2)*(3^2)

42=2*3*7

24=(2^3)*3

52=(2^2)*13

The LCM must contain at least one of each prime base found in any of the numbers, and it must have the highest power of that prime seen in the list above.

We see these numbers contain the primes 2, 3, 7, and 13. The highest power of 2 we see is 2^3, and the highest power of 3 is 3^2. 7 and 13 are only to the 1st power.

So the LCM(36, 42, 24, 52)=(2^3)*(3^2)*7*13

Which is 6552 unless I made a mistake.

6552 +9=6561.