Least Common Multiple (LCM) of 123 and 35
The least common multiple (LCM) of 123 and 35 is 4305.
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 123 and 35?
First, calculate the GCD of 123 and 35 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 35 = 3 remainder 18 |
| 2 | 35 ÷ 18 = 1 remainder 17 |
| 3 | 18 ÷ 17 = 1 remainder 1 |
| 4 | 17 ÷ 1 = 17 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 94 | 10058 |
| 76 and 105 | 7980 |
| 137 and 118 | 16166 |
| 184 and 44 | 2024 |
| 114 and 82 | 4674 |