Least Common Multiple (LCM) of 60 and 142
The least common multiple (LCM) of 60 and 142 is 4260.
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 142?
First, calculate the GCD of 60 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 142 = 0 remainder 60 |
| 2 | 142 ÷ 60 = 2 remainder 22 |
| 3 | 60 ÷ 22 = 2 remainder 16 |
| 4 | 22 ÷ 16 = 1 remainder 6 |
| 5 | 16 ÷ 6 = 2 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 66 | 1980 |
| 57 and 182 | 10374 |
| 132 and 88 | 264 |
| 98 and 151 | 14798 |
| 124 and 185 | 22940 |