Least Common Multiple (LCM) of 126 and 155
The least common multiple (LCM) of 126 and 155 is 19530.
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 155?
First, calculate the GCD of 126 and 155 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 155 = 0 remainder 126 |
| 2 | 155 ÷ 126 = 1 remainder 29 |
| 3 | 126 ÷ 29 = 4 remainder 10 |
| 4 | 29 ÷ 10 = 2 remainder 9 |
| 5 | 10 ÷ 9 = 1 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 171 | 5985 |
| 111 and 35 | 3885 |
| 72 and 154 | 5544 |
| 30 and 76 | 1140 |
| 49 and 160 | 7840 |