Least Common Multiple (LCM) of 60 and 23
The least common multiple (LCM) of 60 and 23 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 60 and 23?
First, calculate the GCD of 60 and 23 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 23 = 2 remainder 14 |
| 2 | 23 ÷ 14 = 1 remainder 9 |
| 3 | 14 ÷ 9 = 1 remainder 5 |
| 4 | 9 ÷ 5 = 1 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 157 | 15543 |
| 150 and 165 | 1650 |
| 157 and 46 | 7222 |
| 81 and 185 | 14985 |
| 160 and 40 | 160 |