Least Common Multiple (LCM) of 53 and 129
The least common multiple (LCM) of 53 and 129 is 6837.
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 53 and 129?
First, calculate the GCD of 53 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 129 = 0 remainder 53 |
| 2 | 129 ÷ 53 = 2 remainder 23 |
| 3 | 53 ÷ 23 = 2 remainder 7 |
| 4 | 23 ÷ 7 = 3 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 22 | 1342 |
| 185 and 163 | 30155 |
| 40 and 120 | 120 |
| 93 and 184 | 17112 |
| 37 and 156 | 5772 |