The prime factor decompositions of two numbers , T and U , are showr I below. T=2^6times 11^5times 13^2 U=2^3times 5^8times 7times 11^10times 13 What is the lowest common multiple (LCM) of T and U? Give your answer as a product of its prime factors in index form.

Question

Question

The prime factor decompositions of two numbers , T and U , are showr I below. T=2^6times 11^5times 13^2 U=2^3times 5^8times 7times 11^10times 13 What is the lowest common multiple (LCM) of T and U? Give your answer as a product of its prime factors in index form.

Answer 1

\[ LCM(T, U) = 2^{6} \times 5^{8} \times 7 \times 11^{10} \times 13^{2} \]

Answer 2

## Step 1: We first want to break down both values \(T \) and \( U \) into their readable prime factors. This was given to us: ### **\(T = 2^{6} \times 11^{5} \times 13^{2}\)** ### **\(U = 2^{3} \times 5^{8} \times 7 \times 11^{10} \times 13\)** ## Step 2: The Lowest Common Multiple (LCM) of two numbers is found by taking the highest power of all the prime numbers involved for both numbers. For each prime factor, we take whichever counting is higher from either \( T \) or \( U \) : ### * \( 2^{6} \) for 2 (from \( T \)) ### * \( 5^{8} \) for 5 (from \( U \)) ### * \( 7 \) for 7 (from \( U \)) ### * \( 11^{10} \) for 11 (from \( U \)) ### * \( 13^{2} \) for 13 (from \( T \)) ## Step 3: Combine these prime factors to form our Lowest Common Multiple (LCM).

Question

The prime factor decompositions of two numbers , T and U , are showr I below. T=2^6times 11^5times 13^2 U=2^3times 5^8times 7times 11^10times 13 What is the lowest common multiple (LCM) of T and U? Give your answer as a product of its prime factors in index form.

Answer

Answer

Explain

Hot Questions