Let's solve the problem of finding the Least Common Multiple (LCM) for each of the given pairs of numbers:

1. LCM of 4 and 9:

• Prime factors of 4: $2^2$
• Prime factors of 9: $3^2$

To find the LCM, take the highest powers of all prime factors:

• $LCM = 2^2 \times 3^2 = 4 \times 9 = 36$

So, the LCM of 4 and 9 is 36.

2. LCM of 6 and 8:

• Prime factors of 6: $2 \times 3$
• Prime factors of 8: $2^3$

To find the LCM, take the highest powers of all prime factors:

• $LCM = 2^3 \times 3 = 8 \times 3 = 24$

So, the LCM of 6 and 8 is 24.

3. LCM of 10 and 12:

• Prime factors of 10: $2 \times 5$
• Prime factors of 12: $2^2 \times 3$

To find the LCM, take the highest powers of all prime factors:

• $LCM = 2^2 \times 3 \times 5 = 4 \times 3 \times 5 = 60$

So, the LCM of 10 and 12 is 60.

Would you like more details on how the LCM was calculated?

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