Let \({p}=x^{2} {y}^{3} {z}^{{n}}\) and \({q}=x^{3} {y}^{{m}} {z}^{2}\) , where \(x, {y}, {z}\) are prime numbers. If \(\operatorname{LCM}({p}, {q})=x^{3} {y}^{4} {z}^{3}\) , then the value of \((2 {~m}+3 {n})\) is

Real numbers

Grade Class 10

Question:

Let \({p}=x^{2} {y}^{3} {z}^{{n}}\) and \({q}=x^{3} {y}^{{m}} {z}^{2}\), where \(x, {y}, {z}\) are prime numbers. If \(\operatorname{LCM}({p}, {q})=x^{3} {y}^{4} {z}^{3}\), then the value of \((2 {~m}+3 {n})\) is

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15

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14

Step-by-Step Solution

Key Concept: To find the LCM of numbers expressed in prime factorization form, take the maximum exponent for each prime factor.

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Correct Answer: C

Question:

Step-by-Step Solution

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