Least Common Multiple (LCM) of 23 and 147
The least common multiple (LCM) of 23 and 147 is 3381.
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 23 and 147?
First, calculate the GCD of 23 and 147 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 147 = 0 remainder 23 |
| 2 | 147 ÷ 23 = 6 remainder 9 |
| 3 | 23 ÷ 9 = 2 remainder 5 |
| 4 | 9 ÷ 5 = 1 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 119 | 2856 |
| 166 and 192 | 15936 |
| 45 and 10 | 90 |
| 41 and 70 | 2870 |
| 16 and 59 | 944 |