Least Common Multiple (LCM) of 12 and 13
The least common multiple (LCM) of 12 and 13 is 156.
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 12 and 13?
First, calculate the GCD of 12 and 13 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 12 ÷ 13 = 0 remainder 12 |
| 2 | 13 ÷ 12 = 1 remainder 1 |
| 3 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 147 and 165 | 8085 |
| 169 and 186 | 31434 |
| 172 and 111 | 19092 |
| 170 and 120 | 2040 |
| 90 and 51 | 1530 |