Least Common Multiple (LCM) of 119 and 132
The least common multiple (LCM) of 119 and 132 is 15708.
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 132?
First, calculate the GCD of 119 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 132 = 0 remainder 119 |
| 2 | 132 ÷ 119 = 1 remainder 13 |
| 3 | 119 ÷ 13 = 9 remainder 2 |
| 4 | 13 ÷ 2 = 6 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 84 | 84 |
| 32 and 147 | 4704 |
| 106 and 117 | 12402 |
| 181 and 85 | 15385 |
| 110 and 57 | 6270 |