The common divisors of two integers are all integers that are divisors of both integers.

The greatest common divisor of two integers is the largest integer of all shared divisors of these two integers.

We abbreviate the greatest common divisor as #\mathrm{gcd}#.

Example

Common divisors of #40# and #160#:

#1#, #2#, #4#, #5#, #8#, #10#, #20#, #40#

So #\mathrm{gcd}(40,160)=40#

The multiples of #3# are #3,6,9,12,15,\dots#

So, a multiple of #3# is an integer that can be divided by #3#.

A common multiple of two integers is an integer that is divisible by both integers. An easy-to-find common multiple of two integers, is their product.

The least common multiple of two integers is the smallest positive integer within the common multiples of these two integers.

We abbreviate the least common multiple as #\mathrm{lcm}#.

Example

Multiples of #4#:

#4#, #8#, #12#, #16#, #\ldots#

Multiples of #6#:

#6#, #12#, #18#, #24#, #\ldots#

Common multiples:

#12#, #24#, #36#, #48#, #\ldots#

So #\mathrm{lcm}(4,6)=12#