Least Common Multiple (LCM) of 103 and 60
The least common multiple (LCM) of 103 and 60 is 6180.
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 60?
First, calculate the GCD of 103 and 60 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 60 = 1 remainder 43 |
| 2 | 60 ÷ 43 = 1 remainder 17 |
| 3 | 43 ÷ 17 = 2 remainder 9 |
| 4 | 17 ÷ 9 = 1 remainder 8 |
| 5 | 9 ÷ 8 = 1 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 141 | 19740 |
| 69 and 64 | 4416 |
| 43 and 67 | 2881 |
| 150 and 155 | 4650 |
| 125 and 36 | 4500 |