Least Common Multiple (LCM) of 126 and 51
The least common multiple (LCM) of 126 and 51 is 2142.
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 126 and 51?
First, calculate the GCD of 126 and 51 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 51 = 2 remainder 24 |
| 2 | 51 ÷ 24 = 2 remainder 3 |
| 3 | 24 ÷ 3 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 121 | 4840 |
| 65 and 19 | 1235 |
| 132 and 46 | 3036 |
| 110 and 35 | 770 |
| 196 and 121 | 23716 |