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 |
|---|---|
| 147 and 32 | 4704 |
| 55 and 155 | 1705 |
| 103 and 19 | 1957 |
| 13 and 60 | 780 |
| 172 and 34 | 2924 |