Least Common Multiple (LCM) of 23 and 37
The least common multiple (LCM) of 23 and 37 is 851.
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 23 and 37?
First, calculate the GCD of 23 and 37 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 37 = 0 remainder 23 |
| 2 | 37 ÷ 23 = 1 remainder 14 |
| 3 | 23 ÷ 14 = 1 remainder 9 |
| 4 | 14 ÷ 9 = 1 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 40 | 3320 |
| 146 and 149 | 21754 |
| 51 and 188 | 9588 |
| 165 and 72 | 3960 |
| 89 and 127 | 11303 |