Least Common Multiple (LCM) of 36 and 42
The least common multiple (LCM) of 36 and 42 is 252.
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 36 and 42?
First, calculate the GCD of 36 and 42 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 36 ÷ 42 = 0 remainder 36 |
| 2 | 42 ÷ 36 = 1 remainder 6 |
| 3 | 36 ÷ 6 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 189 | 10962 |
| 140 and 162 | 11340 |
| 128 and 166 | 10624 |
| 177 and 143 | 25311 |
| 111 and 80 | 8880 |