Least Common Multiple (LCM) of 119 and 154
The least common multiple (LCM) of 119 and 154 is 2618.
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 119 and 154?
First, calculate the GCD of 119 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 154 = 0 remainder 119 |
| 2 | 154 ÷ 119 = 1 remainder 35 |
| 3 | 119 ÷ 35 = 3 remainder 14 |
| 4 | 35 ÷ 14 = 2 remainder 7 |
| 5 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 77 | 385 |
| 105 and 165 | 1155 |
| 132 and 127 | 16764 |
| 148 and 170 | 12580 |
| 47 and 180 | 8460 |