Least Common Multiple (LCM) of 106 and 42
The least common multiple (LCM) of 106 and 42 is 2226.
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 106 and 42?
First, calculate the GCD of 106 and 42 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 42 = 2 remainder 22 |
| 2 | 42 ÷ 22 = 1 remainder 20 |
| 3 | 22 ÷ 20 = 1 remainder 2 |
| 4 | 20 ÷ 2 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 62 and 114 | 3534 |
| 112 and 90 | 5040 |
| 176 and 123 | 21648 |
| 172 and 186 | 15996 |
| 112 and 152 | 2128 |