If a -23- 3- b -2 - 3 - 5- c -3n- 5 and LCMa-b-c - 23- 3n- 5- then n-

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HCF and LCM

If a =23× 3, ...

Question

If $a = 2^{3} \times 3$ , $b = 2 \times 3 \times 5$ , $c = 3^{n} \times 5$ and $L C M (a, b, c) = 2^{3} \times 3^{n} \times 5$ , then $n =$

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Solution

Given:
$a = 2^{3} \times 3$
$b = 2 \times 3 \times 5$
$c = 3^{n} \times 5$
$L C M (a, b, c) == 2^{3} \times 3^{n} \times 5$
Since, LCM is the product of the highest power of the common prime factors involving other terms.
Since, $a$ and $b$ consists only one $3$ .
So by comparing the LCM obtained by given LCM,
$n = 2$ .
Hence, the correct option is $B$ .

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If a=23×3, b=2×3×5, c=3n×5 and LCM(a,b,c)=23×3n×5, then n=

Given:a=23×3b=2×3×5c=3n×5LCM(a,b,c)==23×3n×5 Since, LCM is the product of the highest power of the common prime factors involving other terms.Since, a and b consists only one 3.So by comparing the LCM obtained by given LCM, n=2.Hence, the correct option is B.

If $a = 2^{3} \times 3$ , $b = 2 \times 3 \times 5$ , $c = 3^{n} \times 5$ and $L C M (a, b, c) = 2^{3} \times 3^{n} \times 5$ , then $n =$