Least Common Multiple (LCM) of 189 and 74
The least common multiple (LCM) of 189 and 74 is 13986.
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 74?
First, calculate the GCD of 189 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 74 = 2 remainder 41 |
| 2 | 74 ÷ 41 = 1 remainder 33 |
| 3 | 41 ÷ 33 = 1 remainder 8 |
| 4 | 33 ÷ 8 = 4 remainder 1 |
| 5 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 154 | 18018 |
| 189 and 71 | 13419 |
| 158 and 84 | 6636 |
| 161 and 63 | 1449 |
| 28 and 125 | 3500 |