Question

if a = 2³×3,b =2×3×5,c =3_(n)×5 and LCM(a,b,c)=2³×3²×5,then find n

Answer 1

Hope this helps you dear:-)

Answer 2

The value of n is 2

Given:

a=2³ * 3 , b= 2 *3 *5 , c=3^n * 5 and LCM(a,b,c) = 2³ *3² *2

To Find:

The value of n

Solution:

The least common multiple of three numbers is the smallest non-zero common number which is a multiple of all the three numbers.

To find the LCM, we need to consider the greater exponent component of prime numbers in the factorization of the number

From the given numbers, 2³,5,3^n for n≥1 is the highest power of each prime number.

∴ LCM(a,b,c)=2³ * 3^n * 5 -----------(1)

but given that LCM(a,b,c) = 2³ *3² *2 --------------(2)

In comparing (1) and (2)

2³ * 3^n * 5 = 2³ *3² *2

3^n = 3²

⇒n =2

∴The value of n is 2

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