Least Common Multiple (LCM) of 134 and 53
The least common multiple (LCM) of 134 and 53 is 7102.
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 134 and 53?
First, calculate the GCD of 134 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 134 ÷ 53 = 2 remainder 28 |
| 2 | 53 ÷ 28 = 1 remainder 25 |
| 3 | 28 ÷ 25 = 1 remainder 3 |
| 4 | 25 ÷ 3 = 8 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 182 | 16744 |
| 56 and 61 | 3416 |
| 12 and 27 | 108 |
| 179 and 85 | 15215 |
| 178 and 105 | 18690 |