Least Common Multiple (LCM) of 71 and 189
The least common multiple (LCM) of 71 and 189 is 13419.
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 71 and 189?
First, calculate the GCD of 71 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 189 = 0 remainder 71 |
| 2 | 189 ÷ 71 = 2 remainder 47 |
| 3 | 71 ÷ 47 = 1 remainder 24 |
| 4 | 47 ÷ 24 = 1 remainder 23 |
| 5 | 24 ÷ 23 = 1 remainder 1 |
| 6 | 23 ÷ 1 = 23 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 62 | 4216 |
| 45 and 167 | 7515 |
| 110 and 115 | 2530 |
| 113 and 157 | 17741 |
| 55 and 140 | 1540 |