Least Common Multiple (LCM) of 103 and 98
The least common multiple (LCM) of 103 and 98 is 10094.
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 98?
First, calculate the GCD of 103 and 98 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 98 = 1 remainder 5 |
| 2 | 98 ÷ 5 = 19 remainder 3 |
| 3 | 5 ÷ 3 = 1 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 141 | 9165 |
| 95 and 102 | 9690 |
| 164 and 140 | 5740 |
| 141 and 97 | 13677 |
| 113 and 43 | 4859 |