Least Common Multiple (LCM) of 142 and 105
The least common multiple (LCM) of 142 and 105 is 14910.
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 105?
First, calculate the GCD of 142 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 142 ÷ 105 = 1 remainder 37 |
| 2 | 105 ÷ 37 = 2 remainder 31 |
| 3 | 37 ÷ 31 = 1 remainder 6 |
| 4 | 31 ÷ 6 = 5 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 23 | 1541 |
| 115 and 194 | 22310 |
| 148 and 198 | 14652 |
| 164 and 73 | 11972 |
| 49 and 166 | 8134 |