Least Common Multiple (LCM) of 123 and 16
The least common multiple (LCM) of 123 and 16 is 1968.
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 16?
First, calculate the GCD of 123 and 16 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 16 = 7 remainder 11 |
| 2 | 16 ÷ 11 = 1 remainder 5 |
| 3 | 11 ÷ 5 = 2 remainder 1 |
| 4 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 141 | 3948 |
| 119 and 55 | 6545 |
| 64 and 172 | 2752 |
| 134 and 76 | 5092 |
| 113 and 138 | 15594 |