Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 6 and 63 the smallest integer that is 126 that is divisible by both numbers.
Least Common Multiple (LCM) of 6 and 63 is 126.
LCM(6,63) = 126
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 6 and 63. First we will calculate the prime factors of 6 and 63.
Prime Factorization of 6
2 | 6 |
3 | 3 |
1 |
Prime factors of 6 are 2,3. Prime factorization of 6 in exponential form is:
6 = 21×31
Prime Factorization of 63
3 | 63 |
3 | 21 |
7 | 7 |
1 |
Prime factors of 63 are 3,7. Prime factorization of 63 in exponential form is:
63 = 32×71
Now multiplying the highest exponent prime factors to calculate the LCM of 6 and 63.
LCM(6,63) = 21×32×71
LCM(6,63) = 126
Factors of 6
List of positive integer factors of 6 that divides 6 without a remainder.
1, 2, 3, 6
Factors of 63
List of positive integer factors of 63 that divides 63 without a remainder.
1, 3, 7, 9, 21, 63
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6 and 63, than apply into the LCM equation.
GCF(6,63) = 3
LCM(6,63) = ( 6 × 63) / 3
LCM(6,63) = 378 / 3
LCM(6,63) = 126
(i) The LCM of 63 and 6 is associative
LCM of 6 and 63 = LCM of 63 and 6
1. What is the LCM of 6 and 63?
Answer: LCM of 6 and 63 is 126.
2. What are the Factors of 6?
Answer: Factors of 6 are 1, 2, 3, 6. There are 4 integers that are factors of 6. The greatest factor of 6 is 6.
3. What are the Factors of 63?
Answer: Factors of 63 are 1, 3, 7, 9, 21, 63. There are 6 integers that are factors of 63. The greatest factor of 63 is 63.
4. How to Find the LCM of 6 and 63?
Answer:
Least Common Multiple of 6 and 63 = 126
Step 1: Find the prime factorization of 6
6 = 2 x 3
Step 2: Find the prime factorization of 63
63 = 3 x 3 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 = 126 = 2 x 3 x 3 x 7
Step 4: Therefore, the least common multiple of 6 and 63 is 126.