Q. 1

# Let's find L.C.M. of 4a^{2}b^{4}c, 12a^{3}bc^{5} and 18a^{2}b^{3}c^{2}

Answer :

Let us understand what L.C.M, Least Common Multiple is.

Least common multiple of two or more integers, is the smallest positive integer that is divisible by these two or more integers.

In order to find L.C.M, we need to find factors of each terms.

Factorization of 4a^{2}b^{4}c = 2 × 2 × a × a × b × b × b × b × c

Or, Factorization of 4a^{2}b^{4}c = 2^{2} × a^{2} × b^{4} × c

Factorization of 12a^{3}bc^{5} = 2 × 2 × 3 × a × a × a × b × c × c × c × c × c

Or, Factorization of 12a^{3}bc^{5} = 2^{2} × 3 × a^{3} × b × c^{5}

Factorization of 18a^{2}b^{3}c^{2} = 2 × 3 × 3 × a × a × b × b × b × c × c

Or, Factorization of 18a^{2}b^{3}c^{2} = 2 × 3^{2} × a^{2} × b^{3} × c^{2}

Now, we need to find the factor of highest power.

Factors of 4a^{2}b^{4}c = 2^{2}, a^{2}, b^{4}, c

Factors of 12a^{3}bc^{5} = 2^{2}, 3, a^{3}, b, c^{5}

Factors of 18a^{2}b^{3}c^{2} = 2, 3^{2}, a^{2}, b^{3}, c^{2}

The factors are 2^{2}, 3^{2}, a^{3}, b^{4} and c^{5}.

By multiplying these factors, we get

2^{2} × 3^{2} × a^{3} × b^{4} × c^{5} = 4 × 9 a^{3}b^{4}c^{5}

⇒ 2^{2} × 3^{2} × a^{3} × b^{4} × c^{5} = 36 a^{3}b^{4}c^{5}

Thus, lcm of 4a^{2}b^{4}c, 12a^{3}bc^{5} and 18a^{2}b^{3}c^{2} is 36 a^{3}b^{4}c^{5}.

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