Least Common Multiple (LCM) of 123 and 70
The least common multiple (LCM) of 123 and 70 is 8610.
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 70?
First, calculate the GCD of 123 and 70 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 70 = 1 remainder 53 |
| 2 | 70 ÷ 53 = 1 remainder 17 |
| 3 | 53 ÷ 17 = 3 remainder 2 |
| 4 | 17 ÷ 2 = 8 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 73 and 20 | 1460 |
| 128 and 194 | 12416 |
| 131 and 179 | 23449 |
| 182 and 131 | 23842 |
| 74 and 44 | 1628 |