Least Common Multiple (LCM) of 76 and 106
The least common multiple (LCM) of 76 and 106 is 4028.
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 106?
First, calculate the GCD of 76 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 76 ÷ 106 = 0 remainder 76 |
| 2 | 106 ÷ 76 = 1 remainder 30 |
| 3 | 76 ÷ 30 = 2 remainder 16 |
| 4 | 30 ÷ 16 = 1 remainder 14 |
| 5 | 16 ÷ 14 = 1 remainder 2 |
| 6 | 14 ÷ 2 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 41 and 147 | 6027 |
| 59 and 155 | 9145 |
| 150 and 30 | 150 |
| 43 and 186 | 7998 |
| 14 and 112 | 112 |