Least Common Multiple (LCM) of 103 and 142
The least common multiple (LCM) of 103 and 142 is 14626.
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 142?
First, calculate the GCD of 103 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 142 = 0 remainder 103 |
| 2 | 142 ÷ 103 = 1 remainder 39 |
| 3 | 103 ÷ 39 = 2 remainder 25 |
| 4 | 39 ÷ 25 = 1 remainder 14 |
| 5 | 25 ÷ 14 = 1 remainder 11 |
| 6 | 14 ÷ 11 = 1 remainder 3 |
| 7 | 11 ÷ 3 = 3 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 160 | 2400 |
| 54 and 31 | 1674 |
| 163 and 70 | 11410 |
| 192 and 11 | 2112 |
| 76 and 114 | 228 |