Least Common Multiple (LCM) of 100 and 119
The least common multiple (LCM) of 100 and 119 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 100 and 119?
First, calculate the GCD of 100 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 119 = 0 remainder 100 |
| 2 | 119 ÷ 100 = 1 remainder 19 |
| 3 | 100 ÷ 19 = 5 remainder 5 |
| 4 | 19 ÷ 5 = 3 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 131 | 2358 |
| 70 and 87 | 6090 |
| 139 and 139 | 139 |
| 33 and 103 | 3399 |
| 46 and 42 | 966 |