Least Common Multiple (LCM) of 119 and 78
The least common multiple (LCM) of 119 and 78 is 9282.
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 78?
First, calculate the GCD of 119 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 78 = 1 remainder 41 |
| 2 | 78 ÷ 41 = 1 remainder 37 |
| 3 | 41 ÷ 37 = 1 remainder 4 |
| 4 | 37 ÷ 4 = 9 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 102 | 10914 |
| 28 and 178 | 2492 |
| 72 and 166 | 5976 |
| 106 and 122 | 6466 |
| 33 and 64 | 2112 |