Least Common Multiple (LCM) of 153 and 178
The least common multiple (LCM) of 153 and 178 is 27234.
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 153 and 178?
First, calculate the GCD of 153 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 153 ÷ 178 = 0 remainder 153 |
| 2 | 178 ÷ 153 = 1 remainder 25 |
| 3 | 153 ÷ 25 = 6 remainder 3 |
| 4 | 25 ÷ 3 = 8 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 82 and 126 | 5166 |
| 90 and 107 | 9630 |
| 152 and 54 | 4104 |
| 110 and 21 | 2310 |
| 147 and 88 | 12936 |