Least Common Multiple (LCM) of 142 and 111
The least common multiple (LCM) of 142 and 111 is 15762.
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 142 and 111?
First, calculate the GCD of 142 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 142 ÷ 111 = 1 remainder 31 |
| 2 | 111 ÷ 31 = 3 remainder 18 |
| 3 | 31 ÷ 18 = 1 remainder 13 |
| 4 | 18 ÷ 13 = 1 remainder 5 |
| 5 | 13 ÷ 5 = 2 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 46 and 76 | 1748 |
| 109 and 144 | 15696 |
| 195 and 107 | 20865 |
| 181 and 194 | 35114 |
| 99 and 98 | 9702 |