Least Common Multiple (LCM) of 137 and 153
The least common multiple (LCM) of 137 and 153 is 20961.
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 137 and 153?
First, calculate the GCD of 137 and 153 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 153 = 0 remainder 137 |
| 2 | 153 ÷ 137 = 1 remainder 16 |
| 3 | 137 ÷ 16 = 8 remainder 9 |
| 4 | 16 ÷ 9 = 1 remainder 7 |
| 5 | 9 ÷ 7 = 1 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 41 and 103 | 4223 |
| 111 and 108 | 3996 |
| 107 and 175 | 18725 |
| 171 and 114 | 342 |
| 72 and 142 | 5112 |