If a - 23- 3- b - 2- 3- 5- c - 3n- 5 and LCM a- b- c - 23- 32- 5- then n - -Here- n is a natural number

Given: a = 2^3× 3 b = 2× 3× 5 c = 3^n× 5 LCM (a, b, c) = 2^3× 3^2× 5 ... (1) Since, to find LCM we need to take the prime fac ...

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Byju's Answer

Standard X

Mathematics

The Fundamental Theorem of Arithmetic

If a = 23× 3,...

Question

If a = $2^{3} \times 3$ , b = $2 \times 3 \times 5$ , c = $3^{n} \times 5$ and LCM (a, b, c) = $2^{3} \times 3^{2} \times 5$ , then n = ?
(Here, n is a natural number)

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Solution

The correct option is B 2
Given: a = $2^{3} \times 3$
b = $2 \times 3 \times 5$
c = $3^{n} \times 5$
LCM (a, b, c) = $2^{3} \times 3^{2} \times 5$ ... (1)
Since, to find LCM we need to take the prime factors with their highest degree:
LCM will be $2^{3} \times 3^{n} \times 5$ ... (2) $(n \geq 1)$
On comparing we get,
n = 2

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If a = 23×3, b = 2×3×5, c = 3n×5 and LCM (a, b, c) = 23×32×5, then n = ? (Here, n is a natural number)

The correct option is B 2Given: a = 23×3 b = 2×3×5 c = 3n×5 LCM (a, b, c) = 23×32×5 ... (1) Since, to find LCM we need to take the prime factors with their highest degree: LCM will be 23×3n×5 ... (2) (n≥1) On comparing we get, n = 2

If a = $2^{3} \times 3$ , b = $2 \times 3 \times 5$ , c = $3^{n} \times 5$ and LCM (a, b, c) = $2^{3} \times 3^{2} \times 5$ , then n = ?
(Here, n is a natural number)