Least Common Multiple (LCM) of 106 and 51
The least common multiple (LCM) of 106 and 51 is 5406.
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 51?
First, calculate the GCD of 106 and 51 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 51 = 2 remainder 4 |
| 2 | 51 ÷ 4 = 12 remainder 3 |
| 3 | 4 ÷ 3 = 1 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 68 | 9180 |
| 178 and 53 | 9434 |
| 20 and 109 | 2180 |
| 59 and 149 | 8791 |
| 42 and 111 | 1554 |