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 |
|---|---|
| 129 and 178 | 22962 |
| 152 and 54 | 4104 |
| 71 and 31 | 2201 |
| 182 and 107 | 19474 |
| 38 and 142 | 2698 |