Least Common Multiple (LCM) of 109 and 142
The least common multiple (LCM) of 109 and 142 is 15478.
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 109 and 142?
First, calculate the GCD of 109 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 142 = 0 remainder 109 |
| 2 | 142 ÷ 109 = 1 remainder 33 |
| 3 | 109 ÷ 33 = 3 remainder 10 |
| 4 | 33 ÷ 10 = 3 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 50 | 600 |
| 162 and 64 | 5184 |
| 96 and 107 | 10272 |
| 138 and 130 | 8970 |
| 12 and 145 | 1740 |