Least Common Multiple (LCM) of 126 and 91
The least common multiple (LCM) of 126 and 91 is 1638.
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 91?
First, calculate the GCD of 126 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 91 = 1 remainder 35 |
| 2 | 91 ÷ 35 = 2 remainder 21 |
| 3 | 35 ÷ 21 = 1 remainder 14 |
| 4 | 21 ÷ 14 = 1 remainder 7 |
| 5 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 38 and 49 | 1862 |
| 167 and 187 | 31229 |
| 182 and 71 | 12922 |
| 105 and 67 | 7035 |
| 102 and 174 | 2958 |