Least Common Multiple (LCM) of 60 and 149
The least common multiple (LCM) of 60 and 149 is 8940.
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 149?
First, calculate the GCD of 60 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 149 = 0 remainder 60 |
| 2 | 149 ÷ 60 = 2 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 |
|---|---|
| 11 and 142 | 1562 |
| 105 and 107 | 11235 |
| 83 and 14 | 1162 |
| 155 and 178 | 27590 |
| 84 and 15 | 420 |