Other Ways to Solve
Least common multiple (LCM) by prime factorization
1. Find the prime factors of 6
The prime factors of 6 are 2 and 3.
2. Find the prime factors of 8
The prime factors of 8 are 2, 2 and 2.
3. Find the prime factors of 42
The prime factors of 42 are 2, 3 and 7.
4. Build a prime factors table
Determine the maximum number of times each prime factor (2, 3, 7) occurs in the factorization of the given numbers:
| Prime factorNumber | 6 | 8 | 42 | Max. occurrence |
| 2 | 1 | 3 | 1 | 3 |
| 3 | 1 | 0 | 1 | 1 |
| 7 | 0 | 0 | 1 | 1 |
The prime factors 3 and 7 occur one time, while 2 occurs more than once.
5. Calculate the LCM
The least common multiple is the product of all factors in the greatest number of their occurrence.
LCM =
LCM =
LCM = 168
The least common multiple of 6, 8 and 42 is 168.
FAQs
Calculate the LCM
The least common multiple of 6, 8 and 42 is 168.
What is the LCM of 8 and 42 using prime factorization? ›
Prime factorization of 8 and 42 is (2 × 2 × 2) = 23 and (2 × 3 × 7) = 21 × 31 × 71 respectively. LCM of 8 and 42 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 23 × 31 × 71 = 168. Hence, the LCM of 8 and 42 by prime factorization is 168.
What is the LCM of 16 and 42 using prime factorization? ›
The LCM of 16 and 42 is the product of all prime numbers on the left, i.e. LCM(16, 42) by division method = 2 × 2 × 2 × 2 × 3 × 7 = 336.
What is the LCM of 6 and 8 using prime factorization? ›
How do you find the LCM of 6 and 8 by Prime Factorization? LCM = 2 × 2 × 2 × 3 = 24.
What is the LCM of 6 8 and 45 by prime factorization method? ›
We use the simultaneous factorisation to find the greatest common factor of 6,8 and 45. We have to divide both of them with possible primes which can divide both of them. The LCM is 2×3×2×2×3×5=360. Therefore, the least common multiple of 6, 8 and 45 is 360.
What is the LCM of 6 18 and 42? ›
Answer: 126 is the smallest number that is divisible by both 18 and 42. What is the LCM for 2, 6, 18 and 42? Answer: LCM for 2, 6, 18 and 42 is 126 as 2 and 6 are also the factors of 18 and 42.
What is the prime factorization 42? ›
The prime factorization of 42 is 2 × 3 × 7.
How to find the LCM using prime factorization? ›
Find the LCM using the prime factors method.
- Find the prime factorization of each number.
- Write each number as a product of primes, matching primes vertically when possible.
- Bring down the primes in each column.
- Multiply the factors to get the LCM.
Answer: The least common multiple 72 is a product of common & odd prime factors between the integers which is divisible by each one an integer of this same group.
What is the LCM of 24 36 and 42 using prime factorization? ›
The least common multiple of 24, 42 and 36 is 504.
504 is the lcm of 18, 24 and 42.
What is the LCM of 36 42 and 148 by prime factorization method? ›
Hence, L. C. M=2×2×3×3×7×37=9324.
What is the LCM of 6 8 12 by prime factorization? ›
LCM of 6, 8, and 12 by Prime Factorization
LCM of 6, 8, and 12 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 23 × 31 = 24. Hence, the LCM of 6, 8, and 12 by prime factorization is 24.
What is the LCM of 8 6 4 12 by prime factorization method? ›
Hence, the LCM is 24.
What is the prime factorization of 8? ›
What is the prime factorization of 8? The prime factorization of 8 is 2 × 2 × 2 or 23.
Is the LCM of 6 and 7 42? ›
LCM of 6 and 7 is 42.
What is the LCM of 6 8 40? ›
Calculate the LCM
The least common multiple of 6, 8 and 40 is 120.
How to find the LCM of 6, 8 and 12? ›
The least common multiple of 6, 8 and 12 is 24. Therefore the smallest number that is divisible by 6, 8, 12 exactly is 24.
What is the LCM of 8 2 4 and 6? ›
Consider the example for finding the LCM of 2, 4, 6 and 8. The answer is 24. 24 is the first/smallest/least number that is commonly divisible by 2, 4, 6 and 8. One can use the Prime Factorization and Division method to find the LCM for the given set of numbers.
