Least Common Multiple (LCM) of 113 and 120
The least common multiple (LCM) of 113 and 120 is 13560.
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 120?
First, calculate the GCD of 113 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 120 = 0 remainder 113 |
| 2 | 120 ÷ 113 = 1 remainder 7 |
| 3 | 113 ÷ 7 = 16 remainder 1 |
| 4 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 175 | 18025 |
| 72 and 72 | 72 |
| 192 and 96 | 192 |
| 43 and 185 | 7955 |
| 102 and 189 | 6426 |