Least Common Multiple (LCM) of 103 and 91
The least common multiple (LCM) of 103 and 91 is 9373.
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 91?
First, calculate the GCD of 103 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 91 = 1 remainder 12 |
| 2 | 91 ÷ 12 = 7 remainder 7 |
| 3 | 12 ÷ 7 = 1 remainder 5 |
| 4 | 7 ÷ 5 = 1 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 129 | 1935 |
| 109 and 183 | 19947 |
| 50 and 143 | 7150 |
| 39 and 35 | 1365 |
| 82 and 117 | 9594 |