Least Common Multiple (LCM) of 103 and 149
The least common multiple (LCM) of 103 and 149 is 15347.
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 149?
First, calculate the GCD of 103 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 149 = 0 remainder 103 |
| 2 | 149 ÷ 103 = 1 remainder 46 |
| 3 | 103 ÷ 46 = 2 remainder 11 |
| 4 | 46 ÷ 11 = 4 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 112 | 4816 |
| 90 and 56 | 2520 |
| 36 and 43 | 1548 |
| 18 and 119 | 2142 |
| 98 and 39 | 3822 |