Least Common Multiple (LCM) of 178 and 21
The least common multiple (LCM) of 178 and 21 is 3738.
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 178 and 21?
First, calculate the GCD of 178 and 21 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 21 = 8 remainder 10 |
| 2 | 21 ÷ 10 = 2 remainder 1 |
| 3 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 21 | 1743 |
| 41 and 76 | 3116 |
| 126 and 93 | 3906 |
| 134 and 183 | 24522 |
| 72 and 20 | 360 |