Least Common Multiple (LCM) of 78 and 123
The least common multiple (LCM) of 78 and 123 is 3198.
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 78 and 123?
First, calculate the GCD of 78 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 123 = 0 remainder 78 |
| 2 | 123 ÷ 78 = 1 remainder 45 |
| 3 | 78 ÷ 45 = 1 remainder 33 |
| 4 | 45 ÷ 33 = 1 remainder 12 |
| 5 | 33 ÷ 12 = 2 remainder 9 |
| 6 | 12 ÷ 9 = 1 remainder 3 |
| 7 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 118 | 11092 |
| 119 and 119 | 119 |
| 175 and 77 | 1925 |
| 152 and 55 | 8360 |
| 113 and 164 | 18532 |