Least Common Multiple (LCM) of 67 and 60
The least common multiple (LCM) of 67 and 60 is 4020.
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 67 and 60?
First, calculate the GCD of 67 and 60 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 60 = 1 remainder 7 |
| 2 | 60 ÷ 7 = 8 remainder 4 |
| 3 | 7 ÷ 4 = 1 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 110 | 9790 |
| 87 and 10 | 870 |
| 98 and 77 | 1078 |
| 156 and 200 | 7800 |
| 171 and 95 | 855 |