Write down the LCM of the following numbers, give your answer in exponential form. $$ A=2^{9} imes 3^{6} imes 5^{4} imes 11^{3} $$ $$ B=2^{2} imes 3^{7} imes 7^{2} $$ $$ C=2^{7} imes 3^{3} imes 13^{3} $$

Question

Write down the LCM of the following numbers, give your answer in exponential form. $$ A=2^{9} 	imes 3^{6} 	imes 5^{4} 	imes 11^{3} $$ $$ B=2^{2} 	imes 3^{7} 	imes 7^{2} $$ $$ C=2^{7} 	imes 3^{3} 	imes 13^{3} $$

UpStudy AI · Accepted Answer

1. Write each number in its prime factorization:
   - $$ A = 2^9 \times 3^6 \times 5^4 \times 11^3 $$
   - $$ B = 2^2 \times 3^7 \times 7^2 $$
   - $$ C = 2^7 \times 3^3 \times 13^3 $$

2. For the least common multiple (LCM), we take each prime factor raised to the highest power that appears in any of the factorizations:
   - For $$2$$: The highest exponent is $$9$$ (from $$A$$).
   - For $$3$$: The highest exponent is $$7$$ (from $$B$$).
   - For $$5$$: The highest exponent is $$4$$ (from $$A$$).
   - For $$7$$: The highest exponent is $$2$$ (from $$B$$).
   - For $$11$$: The highest exponent is $$3$$ (from $$A$$).
   - For $$13$$: The highest exponent is $$3$$ (from $$C$$).

3. Therefore, the LCM is:
   $$
   2^9 \times 3^7 \times 5^4 \times 7^2 \times 11^3 \times 13^3
   $$
The LCM of the numbers is $$ 2^9 \times 3^7 \times 5^4 \times 7^2 \times 11^3 \times 13^3 $$.

Write down the LCM of the following numbers, give your answer in exponential form. \( A=2^{9} \times 3^{6} \times 5^{4} \times 11^{3} \) \( B=2^{2} \times 3^{7} \times 7^{2} \) \( C=2^{7} \times 3^{3} \times 13^{3} \)

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