Least Common Multiple (LCM) of 36 and 119
The least common multiple (LCM) of 36 and 119 is 4284.
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 36 and 119?
First, calculate the GCD of 36 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 36 ÷ 119 = 0 remainder 36 |
| 2 | 119 ÷ 36 = 3 remainder 11 |
| 3 | 36 ÷ 11 = 3 remainder 3 |
| 4 | 11 ÷ 3 = 3 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 105 | 19635 |
| 142 and 178 | 12638 |
| 127 and 137 | 17399 |
| 164 and 187 | 30668 |
| 197 and 60 | 11820 |