Least Common Multiple (LCM) of 110 and 142
The least common multiple (LCM) of 110 and 142 is 7810.
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 110 and 142?
First, calculate the GCD of 110 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 142 = 0 remainder 110 |
| 2 | 142 ÷ 110 = 1 remainder 32 |
| 3 | 110 ÷ 32 = 3 remainder 14 |
| 4 | 32 ÷ 14 = 2 remainder 4 |
| 5 | 14 ÷ 4 = 3 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 89 | 8900 |
| 70 and 85 | 1190 |
| 129 and 102 | 4386 |
| 93 and 55 | 5115 |
| 89 and 88 | 7832 |