Least Common Multiple (LCM) of 196 and 123
The least common multiple (LCM) of 196 and 123 is 24108.
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 196 and 123?
First, calculate the GCD of 196 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 196 ÷ 123 = 1 remainder 73 |
| 2 | 123 ÷ 73 = 1 remainder 50 |
| 3 | 73 ÷ 50 = 1 remainder 23 |
| 4 | 50 ÷ 23 = 2 remainder 4 |
| 5 | 23 ÷ 4 = 5 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 93 and 143 | 13299 |
| 56 and 174 | 4872 |
| 62 and 102 | 3162 |
| 128 and 36 | 1152 |
| 31 and 184 | 5704 |