ind the LCM of the following: $$ 3^{2} imes 2^{4} imes 5 $$ and $$ 3 imes 2^{3} imes 5^{2} $$

Question

ind the LCM of the following: $$ 3^{2} 	imes 2^{4} 	imes 5 $$ and $$ 3 	imes 2^{3} 	imes 5^{2} $$

UpStudy AI · Accepted Answer

1. Write the numbers in prime factorization form:

- First number: $$ 3^{2} \times 2^{4} \times 5^{1} $$
   - Second number: $$ 3^{1} \times 2^{3} \times 5^{2} $$

2. For each prime, take the maximum exponent found in the two numbers:

- For $$3$$: maximum exponent is $$2$$.
   - For $$2$$: maximum exponent is $$4$$.
   - For $$5$$: maximum exponent is $$2$$.

3. Multiply the primes raised to these powers to get the LCM:

$$
   \text{LCM} = 3^{2} \times 2^{4} \times 5^{2}
   $$

4. Calculate the numerical value:

$$
   3^{2} = 9,\quad 2^{4} = 16,\quad 5^{2} = 25
   $$
   
   $$
   \text{LCM} = 9 \times 16 \times 25 = 144 \times 25 = 3600
   $$

Thus, the LCM is $$ 3600 $$.
The LCM is 3600.

ind the LCM of the following: \( 3^{2} \times 2^{4} \times 5 \) and \( 3 \times 2^{3} \times 5^{2} \)