Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 63 and 77 the smallest integer that is 693 that is divisible by both numbers.
Least Common Multiple (LCM) of 63 and 77 is 693.
LCM(63,77) = 693
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 63 and 77. First we will calculate the prime factors of 63 and 77.
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
Prime Factorization of 77
7 | 77 |
11 | 11 |
1 |
Prime factors of 77 are 7,11. Prime factorization of 77 in exponential form is:
77 = 71×111
Now multiplying the highest exponent prime factors to calculate the LCM of 63 and 77.
LCM(63,77) = 32×71×111
LCM(63,77) = 693
Factors of 63
List of positive integer factors of 63 that divides 63 without a remainder.
1, 3, 7, 9, 21, 63
Factors of 77
List of positive integer factors of 77 that divides 77 without a remainder.
1, 7, 11, 77
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 63 and 77, than apply into the LCM equation.
GCF(63,77) = 7
LCM(63,77) = ( 63 × 77) / 7
LCM(63,77) = 4851 / 7
LCM(63,77) = 693
(i) The LCM of 77 and 63 is associative
LCM of 63 and 77 = LCM of 77 and 63
1. What is the LCM of 63 and 77?
Answer: LCM of 63 and 77 is 693.
2. 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.
3. What are the Factors of 77?
Answer: Factors of 77 are 1, 7, 11, 77. There are 4 integers that are factors of 77. The greatest factor of 77 is 77.
4. How to Find the LCM of 63 and 77?
Answer:
Least Common Multiple of 63 and 77 = 693
Step 1: Find the prime factorization of 63
63 = 3 x 3 x 7
Step 2: Find the prime factorization of 77
77 = 7 x 11
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 693 = 3 x 3 x 7 x 11
Step 4: Therefore, the least common multiple of 63 and 77 is 693.