Least Common Multiple (LCM) of 60 and 167
The least common multiple (LCM) of 60 and 167 is 10020.
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 167?
First, calculate the GCD of 60 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 167 = 0 remainder 60 |
| 2 | 167 ÷ 60 = 2 remainder 47 |
| 3 | 60 ÷ 47 = 1 remainder 13 |
| 4 | 47 ÷ 13 = 3 remainder 8 |
| 5 | 13 ÷ 8 = 1 remainder 5 |
| 6 | 8 ÷ 5 = 1 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 179 | 25418 |
| 86 and 167 | 14362 |
| 105 and 190 | 3990 |
| 153 and 47 | 7191 |
| 58 and 185 | 10730 |