Least Common Multiple (LCM) of 13 and 60
The least common multiple (LCM) of 13 and 60 is 780.
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 13 and 60?
First, calculate the GCD of 13 and 60 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 13 ÷ 60 = 0 remainder 13 |
| 2 | 60 ÷ 13 = 4 remainder 8 |
| 3 | 13 ÷ 8 = 1 remainder 5 |
| 4 | 8 ÷ 5 = 1 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 158 and 11 | 1738 |
| 52 and 27 | 1404 |
| 106 and 11 | 1166 |
| 151 and 193 | 29143 |
| 30 and 25 | 150 |