Least Common Multiple (LCM) of 51 and 119
The least common multiple (LCM) of 51 and 119 is 357.
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 51 and 119?
First, calculate the GCD of 51 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 119 = 0 remainder 51 |
| 2 | 119 ÷ 51 = 2 remainder 17 |
| 3 | 51 ÷ 17 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 87 | 11310 |
| 119 and 104 | 12376 |
| 132 and 176 | 528 |
| 89 and 171 | 15219 |
| 39 and 173 | 6747 |