Least Common Multiple (LCM) of 103 and 120
The least common multiple (LCM) of 103 and 120 is 12360.
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 103 and 120?
First, calculate the GCD of 103 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 120 = 0 remainder 103 |
| 2 | 120 ÷ 103 = 1 remainder 17 |
| 3 | 103 ÷ 17 = 6 remainder 1 |
| 4 | 17 ÷ 1 = 17 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 153 and 111 | 5661 |
| 112 and 122 | 6832 |
| 115 and 101 | 11615 |
| 30 and 14 | 210 |
| 66 and 158 | 5214 |