Least Common Multiple (LCM) of 76 and 119
The least common multiple (LCM) of 76 and 119 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 76 and 119?
First, calculate the GCD of 76 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 76 ÷ 119 = 0 remainder 76 |
| 2 | 119 ÷ 76 = 1 remainder 43 |
| 3 | 76 ÷ 43 = 1 remainder 33 |
| 4 | 43 ÷ 33 = 1 remainder 10 |
| 5 | 33 ÷ 10 = 3 remainder 3 |
| 6 | 10 ÷ 3 = 3 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 97 and 87 | 8439 |
| 57 and 112 | 6384 |
| 126 and 85 | 10710 |
| 150 and 192 | 4800 |
| 87 and 179 | 15573 |