Least Common Multiple (LCM) of 72 and 149
The least common multiple (LCM) of 72 and 149 is 10728.
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 72 and 149?
First, calculate the GCD of 72 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 149 = 0 remainder 72 |
| 2 | 149 ÷ 72 = 2 remainder 5 |
| 3 | 72 ÷ 5 = 14 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 52 | 7020 |
| 110 and 151 | 16610 |
| 195 and 195 | 195 |
| 23 and 103 | 2369 |
| 100 and 22 | 1100 |