Least Common Multiple (LCM) of 32 and 37
The least common multiple (LCM) of 32 and 37 is 1184.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 32 and 37?
First, calculate the GCD of 32 and 37 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 32 ÷ 37 = 0 remainder 32 |
| 2 | 37 ÷ 32 = 1 remainder 5 |
| 3 | 32 ÷ 5 = 6 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 146 | 7154 |
| 31 and 69 | 2139 |
| 158 and 65 | 10270 |
| 166 and 125 | 20750 |
| 108 and 179 | 19332 |