Least Common Multiple (LCM) of 113 and 60
The least common multiple (LCM) of 113 and 60 is 6780.
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 113 and 60?
First, calculate the GCD of 113 and 60 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 60 = 1 remainder 53 |
| 2 | 60 ÷ 53 = 1 remainder 7 |
| 3 | 53 ÷ 7 = 7 remainder 4 |
| 4 | 7 ÷ 4 = 1 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 121 | 24079 |
| 89 and 123 | 10947 |
| 65 and 48 | 3120 |
| 111 and 70 | 7770 |
| 65 and 59 | 3835 |