Question

find the smallest value of n such that the LCM of n and 6 is 24​

Answer 1

Answer:

8

Step-by-step explanation:

Since 24 is the LCM of 6 and n, 24 is a multiple of n. Now:

1. LCM(6,1)=6;

2. LCM(6,2)=6;

3. LCM(6,3)=6;

4. LCM(6,4)=12;

5. LCM(6,6)=6;

6. LCM(6,8)=24.

So, n = 8.

OR

Through Prime Factorisation:

6 = 2 ⋅ 3, 24 = 2³ ⋅ 3.

Now, the least common multiple of 6 and some number n needs to yield a prime factorization of 2³ ⋅ 3. Note that the prime factorization of the least common multiple between two numbers will be the largest exponent of each prime between the two numbers. So, in this case, we need n to have 3 factors of 2 and up to 1 factor of 3.

This implies that there are 2 such integers n that will work. Namely, 8 and 24. The smaller of these two is 8.

Answer 2

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