Least Common Multiple (LCM) of 119 and 76
The least common multiple (LCM) of 119 and 76 is 9044.
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 76?
First, calculate the GCD of 119 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 76 = 1 remainder 43 |
| 2 | 76 ÷ 43 = 1 remainder 33 |
| 3 | 43 ÷ 33 = 1 remainder 10 |
| 4 | 33 ÷ 10 = 3 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 199 | 11940 |
| 77 and 195 | 15015 |
| 73 and 146 | 146 |
| 123 and 34 | 4182 |
| 107 and 162 | 17334 |