Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 28 and 35 the smallest integer that is 140 that is divisible by both numbers.
Least Common Multiple (LCM) of 28 and 35 is 140.
LCM(28,35) = 140
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 28 and 35. First we will calculate the prime factors of 28 and 35.
Prime Factorization of 28
2 | 28 |
2 | 14 |
7 | 7 |
1 |
Prime factors of 28 are 2,7. Prime factorization of 28 in exponential form is:
28 = 22×71
Prime Factorization of 35
5 | 35 |
7 | 7 |
1 |
Prime factors of 35 are 5,7. Prime factorization of 35 in exponential form is:
35 = 51×71
Now multiplying the highest exponent prime factors to calculate the LCM of 28 and 35.
LCM(28,35) = 22×51×71
LCM(28,35) = 140
Factors of 28
List of positive integer factors of 28 that divides 28 without a remainder.
1, 2, 4, 7, 14, 28
Factors of 35
List of positive integer factors of 35 that divides 35 without a remainder.
1, 5, 7, 35
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 28 and 35, than apply into the LCM equation.
GCF(28,35) = 7
LCM(28,35) = ( 28 × 35) / 7
LCM(28,35) = 980 / 7
LCM(28,35) = 140
(i) The LCM of 35 and 28 is associative
LCM of 28 and 35 = LCM of 35 and 28
1. What is the LCM of 28 and 35?
Answer: LCM of 28 and 35 is 140.
2. What are the Factors of 28?
Answer: Factors of 28 are 1, 2, 4, 7, 14, 28. There are 6 integers that are factors of 28. The greatest factor of 28 is 28.
3. What are the Factors of 35?
Answer: Factors of 35 are 1, 5, 7, 35. There are 4 integers that are factors of 35. The greatest factor of 35 is 35.
4. How to Find the LCM of 28 and 35?
Answer:
Least Common Multiple of 28 and 35 = 140
Step 1: Find the prime factorization of 28
28 = 2 x 2 x 7
Step 2: Find the prime factorization of 35
35 = 5 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 140 = 2 x 2 x 5 x 7
Step 4: Therefore, the least common multiple of 28 and 35 is 140.