Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 33 and 34 the smallest integer that is 1122 that is divisible by both numbers.
Least Common Multiple (LCM) of 33 and 34 is 1122.
LCM(33,34) = 1122
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 33 and 34. First we will calculate the prime factors of 33 and 34.
Prime Factorization of 33
3 | 33 |
11 | 11 |
1 |
Prime factors of 33 are 3,11. Prime factorization of 33 in exponential form is:
33 = 31×111
Prime Factorization of 34
2 | 34 |
17 | 17 |
1 |
Prime factors of 34 are 2,17. Prime factorization of 34 in exponential form is:
34 = 21×171
Now multiplying the highest exponent prime factors to calculate the LCM of 33 and 34.
LCM(33,34) = 21×31×111×171
LCM(33,34) = 1122
Factors of 33
List of positive integer factors of 33 that divides 33 without a remainder.
1, 3, 11, 33
Factors of 34
List of positive integer factors of 34 that divides 34 without a remainder.
1, 2, 17, 34
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 33 and 34, than apply into the LCM equation.
GCF(33,34) = 1
LCM(33,34) = ( 33 × 34) / 1
LCM(33,34) = 1122 / 1
LCM(33,34) = 1122
(i) The LCM of 34 and 33 is associative
LCM of 33 and 34 = LCM of 34 and 33
1. What is the LCM of 33 and 34?
Answer: LCM of 33 and 34 is 1122.
2. What are the Factors of 33?
Answer: Factors of 33 are 1, 3, 11, 33. There are 4 integers that are factors of 33. The greatest factor of 33 is 33.
3. What are the Factors of 34?
Answer: Factors of 34 are 1, 2, 17, 34. There are 4 integers that are factors of 34. The greatest factor of 34 is 34.
4. How to Find the LCM of 33 and 34?
Answer:
Least Common Multiple of 33 and 34 = 1122
Step 1: Find the prime factorization of 33
33 = 3 x 11
Step 2: Find the prime factorization of 34
34 = 2 x 17
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1122 = 2 x 3 x 11 x 17
Step 4: Therefore, the least common multiple of 33 and 34 is 1122.