Finding the LCM of Non-Zero Integers - # 2

[Jason]

What is the LCM of 36 and 48?

\(36 \longrightarrow 4 * 9 \longrightarrow 2 * 2 * 3 * 3 \longrightarrow 2^{2} * 3^{2}\)

\(48 \longrightarrow 16 * 3 \longrightarrow 4 * 4 * 3 \longrightarrow 2 * 2 * 2 * 2 * 3 \longrightarrow 2^{4},\,\,3^{1}\)

The highest pairs of prime power/powers are:

none

The highest solo prime power/powers are:

\(2^{4},\,\,3^{2}\)

\(LCM = 2^{4} * 3^{2} = 144^{1} = 144\)

What is the LCM of 99 & 15?

\(99 \longrightarrow 33 * 3 \longrightarrow (11 * 3) * 3 \longrightarrow 11^{1} * 3^{1} * 3^{1} \longrightarrow 11^{1} * 3^{2} \)

\(15 \longrightarrow 3 * 5 \longrightarrow 3^{1} * 5^{1}\)

The highest pairs of prime power/powers are:

none

The highest solo prime power/powers are:

\(3^{2},\,\, 5^{1},\,\, 11^{1}\)

\(LCM: 3^{2} * 5^{1} * 11^{1} = 495^{1}= 495\)