Least Common Multiple (LCM) of 126 and 153
The least common multiple (LCM) of 126 and 153 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 153?
First, calculate the GCD of 126 and 153 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 153 = 0 remainder 126 |
| 2 | 153 ÷ 126 = 1 remainder 27 |
| 3 | 126 ÷ 27 = 4 remainder 18 |
| 4 | 27 ÷ 18 = 1 remainder 9 |
| 5 | 18 ÷ 9 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 65 | 12480 |
| 35 and 34 | 1190 |
| 121 and 196 | 23716 |
| 35 and 77 | 385 |
| 56 and 177 | 9912 |