Least Common Multiple (LCM) of 120 and 154
The least common multiple (LCM) of 120 and 154 is 9240.
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 154?
First, calculate the GCD of 120 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 154 = 0 remainder 120 |
| 2 | 154 ÷ 120 = 1 remainder 34 |
| 3 | 120 ÷ 34 = 3 remainder 18 |
| 4 | 34 ÷ 18 = 1 remainder 16 |
| 5 | 18 ÷ 16 = 1 remainder 2 |
| 6 | 16 ÷ 2 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 26 | 4810 |
| 19 and 10 | 190 |
| 185 and 20 | 740 |
| 89 and 79 | 7031 |
| 185 and 20 | 740 |