Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 9955 and 9960 the smallest integer that is 19830360 that is divisible by both numbers.
Least Common Multiple (LCM) of 9955 and 9960 is 19830360.
LCM(9955,9960) = 19830360
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 9955 and 9960. First we will calculate the prime factors of 9955 and 9960.
Prime Factorization of 9955
5 | 9955 |
11 | 1991 |
181 | 181 |
1 |
Prime factors of 9955 are 5, 11,181. Prime factorization of 9955 in exponential form is:
9955 = 51×111×1811
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 9955 and 9960.
LCM(9955,9960) = 23×31×51×111×831×1811
LCM(9955,9960) = 19830360
Factors of 9955
List of positive integer factors of 9955 that divides 9955 without a remainder.
1, 5, 11, 55, 181, 905, 1991, 9955
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 9955 and 9960, than apply into the LCM equation.
GCF(9955,9960) = 5
LCM(9955,9960) = ( 9955 × 9960) / 5
LCM(9955,9960) = 99151800 / 5
LCM(9955,9960) = 19830360
(i) The LCM of 9960 and 9955 is associative
LCM of 9955 and 9960 = LCM of 9960 and 9955
1. What is the LCM of 9955 and 9960?
Answer: LCM of 9955 and 9960 is 19830360.
2. What are the Factors of 9955?
Answer: Factors of 9955 are 1, 5, 11, 55, 181, 905, 1991, 9955. There are 8 integers that are factors of 9955. The greatest factor of 9955 is 9955.
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 9955 and 9960?
Answer:
Least Common Multiple of 9955 and 9960 = 19830360
Step 1: Find the prime factorization of 9955
9955 = 5 x 11 x 181
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 = 19830360 = 2 x 2 x 2 x 3 x 5 x 11 x 83 x 181
Step 4: Therefore, the least common multiple of 9955 and 9960 is 19830360.