Least Common Multiple (LCM) of 32 and 23
The least common multiple (LCM) of 32 and 23 is 736.
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 23?
First, calculate the GCD of 32 and 23 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 32 ÷ 23 = 1 remainder 9 |
| 2 | 23 ÷ 9 = 2 remainder 5 |
| 3 | 9 ÷ 5 = 1 remainder 4 |
| 4 | 5 ÷ 4 = 1 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 151 | 17365 |
| 107 and 74 | 7918 |
| 188 and 165 | 31020 |
| 135 and 182 | 24570 |
| 146 and 60 | 4380 |