Least Common Multiple (LCM) of 76 and 189
The least common multiple (LCM) of 76 and 189 is 14364.
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 189?
First, calculate the GCD of 76 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 76 ÷ 189 = 0 remainder 76 |
| 2 | 189 ÷ 76 = 2 remainder 37 |
| 3 | 76 ÷ 37 = 2 remainder 2 |
| 4 | 37 ÷ 2 = 18 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 43 | 129 |
| 162 and 88 | 7128 |
| 158 and 196 | 15484 |
| 124 and 38 | 2356 |
| 146 and 29 | 4234 |