Least Common Multiple (LCM) of 106 and 76
The least common multiple (LCM) of 106 and 76 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 106 and 76?
First, calculate the GCD of 106 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 76 = 1 remainder 30 |
| 2 | 76 ÷ 30 = 2 remainder 16 |
| 3 | 30 ÷ 16 = 1 remainder 14 |
| 4 | 16 ÷ 14 = 1 remainder 2 |
| 5 | 14 ÷ 2 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 56 and 61 | 3416 |
| 186 and 32 | 2976 |
| 112 and 15 | 1680 |
| 182 and 171 | 31122 |
| 120 and 171 | 6840 |