2 36, 89, 90

Question

2 36, 89, 90

ScanSolve AI Tutor · Accepted Answer

Based on the numbers provided, I will assume you need to find the Least Common Multiple (LCM) of $2, 36, 89,$ and 90.

Find the prime factorization of each number.
$2 = 2^{1}$ $36 = 2 \times 18 = 2 \times 2 \times 9 = 2^{2} \times 3^{2}$ $89 = 89^{1} \quad (\text{since } 89 \text{ is a prime number})$ $90 = 2 \times 45 = 2 \times 3 \times 15 = 2 \times 3 \times 3 \times 5 = 2^{1} \times 3^{2} \times 5^{1}$
Identify all unique prime factors and their highest powers from the factorizations.
The unique prime factors are $2, 3, 5,$ and 89.
The highest power of 2 is $2^{2}$ (from 36).
The highest power of 3 is $3^{2}$ (from 36 and 90).
The highest power of 5 is $5^{1}$ (from 90).
The highest power of 89 is $89^{1}$ (from 89).
Multiply these highest powers together to find the LCM.
$\text{LCM} = 2^{2} \times 3^{2} \times 5^{1} \times 89^{1}$ $\text{LCM} = 4 \times 9 \times 5 \times 89$ $\text{LCM} = 36 \times 5 \times 89$ $\text{LCM} = 180 \times 89$
Calculate the final product.
$\text{LCM} = 16020$
The Least Common Multiple (LCM) is $\text{16020}$ .

Answer