# Determine the lowest common multiple (LCM) and the highest common factor (HCF) of the following algebraic terms by using prime factors: 22a^{5}b^{3}c^{2}. 2a^{4}b^{4}c^{3}. 4a^{2}b^{2}c^{5}

Determine the lowest common multiple (LCM) and the highest common factor (HCF) of the following algebraic terms by using prime factors:
$$\displaystyle{22}{a}^{{{5}}}{b}^{{{3}}}{c}^{{{2}}}.{2}{a}^{{{4}}}{b}^{{{4}}}{c}^{{{3}}}.{4}{a}^{{{2}}}{b}^{{{2}}}{c}^{{{5}}}$$

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Caren
Step 1
Given ,
$$\displaystyle{X}={22}{a}^{{{5}}}{b}^{{{3}}}{c}^{{{2}}}$$
$$\displaystyle{Y}={2}{a}^{{{4}}}{b}^{{{4}}}{c}^{{{3}}}$$
$$\displaystyle{Z}={4}{a}^{{{2}}}{b}^{{{2}}}{c}^{{{5}}}$$
Step 2
$$\displaystyle{22}{a}^{{{5}}}{b}^{{{3}}}{c}^{{{2}}}.{2}{a}^{{{4}}}{b}^{{{4}}}{c}^{{{3}}}.{4}{a}^{{{2}}}{b}^{{{2}}}{c}^{{{5}}}$$
Let $$\displaystyle{x}={2}\times{11}\times{a}^{{{5}}}\times{b}^{{{3}}}\times{c}^{{{2}}}$$
$$\displaystyle{y}={2}\times{a}^{{{4}}}\times{b}^{{{4}}}\times{c}^{{{3}}}$$
$$\displaystyle{z}={2}\times{2}\times{a}^{{{2}}}\times{b}^{{{2}}}\times{c}^{{{5}}}$$
$$\displaystyle{L}{C}{M}={2}\times{11}\times{2}\times{a}^{{{5}}}\times{b}^{{{4}}}\times{c}^{{{5}}}$$
$$\displaystyle{L}{C}{M}={44}{a}^{{{5}}}{b}^{{{4}}}{c}^{{{5}}}$$
$$\displaystyle{H}{C}{F}={2}\times{a}^{{{2}}}\times{b}^{{{2}}}\times{c}^{{{2}}}$$
$$\displaystyle{H}{C}{F}={2}{a}^{{{2}}}{b}^{{{2}}}{c}^{{{2}}}$$