Least Common Multiple (LCM) of 50 and 119
The least common multiple (LCM) of 50 and 119 is 5950.
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 50 and 119?
First, calculate the GCD of 50 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 119 = 0 remainder 50 |
| 2 | 119 ÷ 50 = 2 remainder 19 |
| 3 | 50 ÷ 19 = 2 remainder 12 |
| 4 | 19 ÷ 12 = 1 remainder 7 |
| 5 | 12 ÷ 7 = 1 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 200 and 87 | 17400 |
| 196 and 115 | 22540 |
| 23 and 66 | 1518 |
| 171 and 188 | 32148 |
| 76 and 36 | 684 |