Least Common Multiple (LCM) of 60 and 111
The least common multiple (LCM) of 60 and 111 is 2220.
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 111?
First, calculate the GCD of 60 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 111 = 0 remainder 60 |
| 2 | 111 ÷ 60 = 1 remainder 51 |
| 3 | 60 ÷ 51 = 1 remainder 9 |
| 4 | 51 ÷ 9 = 5 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 110 | 1760 |
| 119 and 169 | 20111 |
| 110 and 31 | 3410 |
| 169 and 57 | 9633 |
| 123 and 117 | 4797 |