Least Common Multiple (LCM) of 60 and 89
The least common multiple (LCM) of 60 and 89 is 5340.
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 60 and 89?
First, calculate the GCD of 60 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 89 = 0 remainder 60 |
| 2 | 89 ÷ 60 = 1 remainder 29 |
| 3 | 60 ÷ 29 = 2 remainder 2 |
| 4 | 29 ÷ 2 = 14 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 167 | 19038 |
| 18 and 97 | 1746 |
| 42 and 188 | 3948 |
| 170 and 194 | 16490 |
| 125 and 16 | 2000 |