Least Common Multiple (LCM) of 76 and 142
The least common multiple (LCM) of 76 and 142 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 76 and 142?
First, calculate the GCD of 76 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 76 ÷ 142 = 0 remainder 76 |
| 2 | 142 ÷ 76 = 1 remainder 66 |
| 3 | 76 ÷ 66 = 1 remainder 10 |
| 4 | 66 ÷ 10 = 6 remainder 6 |
| 5 | 10 ÷ 6 = 1 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 183 and 171 | 10431 |
| 117 and 130 | 1170 |
| 99 and 50 | 4950 |
| 184 and 75 | 13800 |
| 42 and 148 | 3108 |