Least Common Multiple (LCM) of 119 and 100
The least common multiple (LCM) of 119 and 100 is 11900.
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 100?
First, calculate the GCD of 119 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 100 = 1 remainder 19 |
| 2 | 100 ÷ 19 = 5 remainder 5 |
| 3 | 19 ÷ 5 = 3 remainder 4 |
| 4 | 5 ÷ 4 = 1 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 127 and 178 | 22606 |
| 133 and 51 | 6783 |
| 181 and 116 | 20996 |
| 152 and 24 | 456 |
| 19 and 72 | 1368 |