Least Common Multiple (LCM) of 12 and 42
The least common multiple (LCM) of 12 and 42 is 84.
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 42?
First, calculate the GCD of 12 and 42 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 12 ÷ 42 = 0 remainder 12 |
| 2 | 42 ÷ 12 = 3 remainder 6 |
| 3 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 172 | 6708 |
| 74 and 147 | 10878 |
| 137 and 29 | 3973 |
| 136 and 73 | 9928 |
| 120 and 105 | 840 |