What is the lcm of these two numbers 2 to the 6th power x 3 to the 4 power x 5 and 2 to the 5th power x 3 to the 7th power x 5? (it also said to write solution using exponents.)

Question

i have no idea what this is supposed to be and its my homework so yeah. Can someone help me please? i'm desperate.

Answer 1

If you think about each of these exponents individually, you can put them together to find the lcm.

For example, 2⁵ and 2⁶. 2⁶ can be written as 2*2⁵, so 2⁶ would be the lcm. You can use similar reasoning to find lcm(3⁴,3⁷) = 3⁷. Of course, don't forget the 5.

Once you have those lcms, you can put them together to find the lcm of the entire thing, (2⁶)(3⁷)(5)

Putting together the expanded forms of the lcms, you get (2*2⁵)(3³*3⁴)(5), which is equivalent. There is no way to divide both original numbers into something with smaller exponents, so this is the lcm.