Least Common Multiple (LCM) of 76 and 141
The least common multiple (LCM) of 76 and 141 is 10716.
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 141?
First, calculate the GCD of 76 and 141 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 76 ÷ 141 = 0 remainder 76 |
| 2 | 141 ÷ 76 = 1 remainder 65 |
| 3 | 76 ÷ 65 = 1 remainder 11 |
| 4 | 65 ÷ 11 = 5 remainder 10 |
| 5 | 11 ÷ 10 = 1 remainder 1 |
| 6 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 103 | 5562 |
| 63 and 28 | 252 |
| 149 and 119 | 17731 |
| 131 and 47 | 6157 |
| 122 and 83 | 10126 |