Least Common Multiple (LCM) of 35 and 127
The least common multiple (LCM) of 35 and 127 is 4445.
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 35 and 127?
First, calculate the GCD of 35 and 127 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 35 ÷ 127 = 0 remainder 35 |
| 2 | 127 ÷ 35 = 3 remainder 22 |
| 3 | 35 ÷ 22 = 1 remainder 13 |
| 4 | 22 ÷ 13 = 1 remainder 9 |
| 5 | 13 ÷ 9 = 1 remainder 4 |
| 6 | 9 ÷ 4 = 2 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 137 | 13700 |
| 89 and 152 | 13528 |
| 180 and 173 | 31140 |
| 169 and 65 | 845 |
| 173 and 161 | 27853 |