Least Common Multiple (LCM) of 120 and 134
The least common multiple (LCM) of 120 and 134 is 8040.
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 120 and 134?
First, calculate the GCD of 120 and 134 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 134 = 0 remainder 120 |
| 2 | 134 ÷ 120 = 1 remainder 14 |
| 3 | 120 ÷ 14 = 8 remainder 8 |
| 4 | 14 ÷ 8 = 1 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 178 | 19402 |
| 46 and 68 | 1564 |
| 51 and 60 | 1020 |
| 133 and 109 | 14497 |
| 35 and 99 | 3465 |