Least Common Multiple (LCM) of 126 and 106
The least common multiple (LCM) of 126 and 106 is 6678.
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 106?
First, calculate the GCD of 126 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 106 = 1 remainder 20 |
| 2 | 106 ÷ 20 = 5 remainder 6 |
| 3 | 20 ÷ 6 = 3 remainder 2 |
| 4 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 72 and 37 | 2664 |
| 137 and 160 | 21920 |
| 185 and 112 | 20720 |
| 166 and 151 | 25066 |
| 20 and 21 | 420 |