Least Common Multiple (LCM) of 12 and 105
The least common multiple (LCM) of 12 and 105 is 420.
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 12 and 105?
First, calculate the GCD of 12 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 12 ÷ 105 = 0 remainder 12 |
| 2 | 105 ÷ 12 = 8 remainder 9 |
| 3 | 12 ÷ 9 = 1 remainder 3 |
| 4 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 53 and 32 | 1696 |
| 192 and 114 | 3648 |
| 123 and 29 | 3567 |
| 117 and 174 | 6786 |
| 111 and 72 | 2664 |