Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 32 and 45 the smallest integer that is 1440 that is divisible by both numbers.
Least Common Multiple (LCM) of 32 and 45 is 1440.
LCM(32,45) = 1440
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 32 and 45. First we will calculate the prime factors of 32 and 45.
Prime Factorization of 32
2 | 32 |
2 | 16 |
2 | 8 |
2 | 4 |
2 | 2 |
1 |
Prime factors of 32 are 2. Prime factorization of 32 in exponential form is:
32 = 25
Prime Factorization of 45
3 | 45 |
3 | 15 |
5 | 5 |
1 |
Prime factors of 45 are 3,5. Prime factorization of 45 in exponential form is:
45 = 32×51
Now multiplying the highest exponent prime factors to calculate the LCM of 32 and 45.
LCM(32,45) = 25×32×51
LCM(32,45) = 1440
Factors of 32
List of positive integer factors of 32 that divides 32 without a remainder.
1, 2, 4, 8, 16, 32
Factors of 45
List of positive integer factors of 45 that divides 45 without a remainder.
1, 3, 5, 9, 15, 45
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 32 and 45, than apply into the LCM equation.
GCF(32,45) = 1
LCM(32,45) = ( 32 × 45) / 1
LCM(32,45) = 1440 / 1
LCM(32,45) = 1440
(i) The LCM of 45 and 32 is associative
LCM of 32 and 45 = LCM of 45 and 32
1. What is the LCM of 32 and 45?
Answer: LCM of 32 and 45 is 1440.
2. What are the Factors of 32?
Answer: Factors of 32 are 1, 2, 4, 8, 16, 32. There are 6 integers that are factors of 32. The greatest factor of 32 is 32.
3. What are the Factors of 45?
Answer: Factors of 45 are 1, 3, 5, 9, 15, 45. There are 6 integers that are factors of 45. The greatest factor of 45 is 45.
4. How to Find the LCM of 32 and 45?
Answer:
Least Common Multiple of 32 and 45 = 1440
Step 1: Find the prime factorization of 32
32 = 2 x 2 x 2 x 2 x 2
Step 2: Find the prime factorization of 45
45 = 3 x 3 x 5
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1440 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5
Step 4: Therefore, the least common multiple of 32 and 45 is 1440.