Least Common Multiple (LCM) of 89 and 147
The least common multiple (LCM) of 89 and 147 is 13083.
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 89 and 147?
First, calculate the GCD of 89 and 147 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 147 = 0 remainder 89 |
| 2 | 147 ÷ 89 = 1 remainder 58 |
| 3 | 89 ÷ 58 = 1 remainder 31 |
| 4 | 58 ÷ 31 = 1 remainder 27 |
| 5 | 31 ÷ 27 = 1 remainder 4 |
| 6 | 27 ÷ 4 = 6 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 61 and 170 | 10370 |
| 144 and 10 | 720 |
| 102 and 140 | 7140 |
| 33 and 126 | 1386 |
| 189 and 66 | 4158 |