Least Common Multiple (LCM) of 60 and 36
The least common multiple (LCM) of 60 and 36 is 180.
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 60 and 36?
First, calculate the GCD of 60 and 36 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 36 = 1 remainder 24 |
| 2 | 36 ÷ 24 = 1 remainder 12 |
| 3 | 24 ÷ 12 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 143 and 180 | 25740 |
| 101 and 157 | 15857 |
| 175 and 113 | 19775 |
| 106 and 127 | 13462 |
| 176 and 63 | 11088 |