Least Common Multiple (LCM) of 23 and 60
The least common multiple (LCM) of 23 and 60 is 1380.
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 60?
First, calculate the GCD of 23 and 60 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 60 = 0 remainder 23 |
| 2 | 60 ÷ 23 = 2 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 |
|---|---|
| 38 and 51 | 1938 |
| 37 and 177 | 6549 |
| 140 and 121 | 16940 |
| 67 and 89 | 5963 |
| 103 and 112 | 11536 |