Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 9953 and 9960 the smallest integer that is 99131880 that is divisible by both numbers.
Least Common Multiple (LCM) of 9953 and 9960 is 99131880.
LCM(9953,9960) = 99131880
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 9953 and 9960. First we will calculate the prime factors of 9953 and 9960.
Prime Factorization of 9953
37 | 9953 |
269 | 269 |
1 |
Prime factors of 9953 are 37,269. Prime factorization of 9953 in exponential form is:
9953 = 371×2691
Prime Factorization of 9960
2 | 9960 |
2 | 4980 |
2 | 2490 |
3 | 1245 |
5 | 415 |
83 | 83 |
1 |
Prime factors of 9960 are 2, 3, 5,83. Prime factorization of 9960 in exponential form is:
9960 = 23×31×51×831
Now multiplying the highest exponent prime factors to calculate the LCM of 9953 and 9960.
LCM(9953,9960) = 23×31×51×371×831×2691
LCM(9953,9960) = 99131880
Factors of 9953
List of positive integer factors of 9953 that divides 9953 without a remainder.
1, 37, 269, 9953
Factors of 9960
List of positive integer factors of 9960 that divides 9960 without a remainder.
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 83, 120, 166, 249, 332, 415, 498, 664, 830, 996, 1245, 1660, 1992, 2490, 3320, 4980, 9960
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9953 and 9960, than apply into the LCM equation.
GCF(9953,9960) = 1
LCM(9953,9960) = ( 9953 × 9960) / 1
LCM(9953,9960) = 99131880 / 1
LCM(9953,9960) = 99131880
(i) The LCM of 9960 and 9953 is associative
LCM of 9953 and 9960 = LCM of 9960 and 9953
1. What is the LCM of 9953 and 9960?
Answer: LCM of 9953 and 9960 is 99131880.
2. What are the Factors of 9953?
Answer: Factors of 9953 are 1, 37, 269, 9953. There are 4 integers that are factors of 9953. The greatest factor of 9953 is 9953.
3. What are the Factors of 9960?
Answer: Factors of 9960 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 83, 120, 166, 249, 332, 415, 498, 664, 830, 996, 1245, 1660, 1992, 2490, 3320, 4980, 9960. There are 32 integers that are factors of 9960. The greatest factor of 9960 is 9960.
4. How to Find the LCM of 9953 and 9960?
Answer:
Least Common Multiple of 9953 and 9960 = 99131880
Step 1: Find the prime factorization of 9953
9953 = 37 x 269
Step 2: Find the prime factorization of 9960
9960 = 2 x 2 x 2 x 3 x 5 x 83
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 99131880 = 2 x 2 x 2 x 3 x 5 x 37 x 83 x 269
Step 4: Therefore, the least common multiple of 9953 and 9960 is 99131880.