Least Common Multiple (LCM) of 126 and 35
The least common multiple (LCM) of 126 and 35 is 630.
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 35?
First, calculate the GCD of 126 and 35 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 35 = 3 remainder 21 |
| 2 | 35 ÷ 21 = 1 remainder 14 |
| 3 | 21 ÷ 14 = 1 remainder 7 |
| 4 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 134 | 13802 |
| 188 and 110 | 10340 |
| 89 and 160 | 14240 |
| 183 and 190 | 34770 |
| 39 and 62 | 2418 |