Least common multiple of 26,39 using prime factorization

26 is a multiple of 2 but 39 isn't

39 is a multiple of 3 but 26 isn't

Dividng by the next three prime numbers, neither 26 nor 39 is a multiple of 5, 7, or 11

Moving up to the sixth prime number (13), we see that BOTH 26 and 39 are divisible by 13.  26 = 2 * 13 and 39 = 3 * 13 and 13 is the lowest common multiple of 26 and 39.

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb