Question

find the lcm of 21y1 and 63y5

Answer 1

what is 21y1 is that\[21y \]and\[63y ^{5}\]

Answer 2

yes

Answer 3

You say 21y by 1, 21y by 2, and on, writing them down. Do the same for 63y^5. Write it down. When you see the same number appear from both lines, that is your number.

Answer 4

It's the case that,\[lcm (a,b)=\frac{a.b}{\gcd(a,b)}\]Now, the greatest common divisor of 21y and 63y^5 is the greatest factor shared between 21y and 63y^5 that divides them. You can use the Euclidean algorithm for more complex case, but here, you can see that 21y divides both 21y and 63y^5. Since 21y is the highest factor of 21y (e.g. like 8 is the highest factor of 8), there are no higher common factors, so \[\gcd(21y,63y^5)=21y\]So you have\[lcm(21y,63y^5)=\frac{21y.63y^5}{21y}=63y^5\]