Least Common Multiple (LCM) of 189 and 76
The least common multiple (LCM) of 189 and 76 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 189 and 76?
First, calculate the GCD of 189 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 76 = 2 remainder 37 |
| 2 | 76 ÷ 37 = 2 remainder 2 |
| 3 | 37 ÷ 2 = 18 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 200 | 20200 |
| 121 and 180 | 21780 |
| 132 and 200 | 6600 |
| 167 and 100 | 16700 |
| 124 and 89 | 11036 |