Least Common Multiple (LCM) of 15 and 119
The least common multiple (LCM) of 15 and 119 is 1785.
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 15 and 119?
First, calculate the GCD of 15 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 15 ÷ 119 = 0 remainder 15 |
| 2 | 119 ÷ 15 = 7 remainder 14 |
| 3 | 15 ÷ 14 = 1 remainder 1 |
| 4 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 143 and 72 | 10296 |
| 193 and 128 | 24704 |
| 200 and 119 | 23800 |
| 11 and 99 | 99 |
| 172 and 182 | 15652 |