Least Common Multiple (LCM) of 142 and 76
The least common multiple (LCM) of 142 and 76 is 5396.
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 76?
First, calculate the GCD of 142 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 142 ÷ 76 = 1 remainder 66 |
| 2 | 76 ÷ 66 = 1 remainder 10 |
| 3 | 66 ÷ 10 = 6 remainder 6 |
| 4 | 10 ÷ 6 = 1 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 38 | 6270 |
| 199 and 85 | 16915 |
| 109 and 47 | 5123 |
| 154 and 86 | 6622 |
| 43 and 105 | 4515 |