Least Common Multiple (LCM) of 156 and 119
The least common multiple (LCM) of 156 and 119 is 18564.
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 156 and 119?
First, calculate the GCD of 156 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 156 ÷ 119 = 1 remainder 37 |
| 2 | 119 ÷ 37 = 3 remainder 8 |
| 3 | 37 ÷ 8 = 4 remainder 5 |
| 4 | 8 ÷ 5 = 1 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 196 | 5292 |
| 90 and 86 | 3870 |
| 37 and 129 | 4773 |
| 99 and 197 | 19503 |
| 180 and 131 | 23580 |