what is the lcm of 6 and 9
LCM of 6 and 9LCM of 6 and 9 is the smallest of all common multiples of 6 and 9. The first multiples of 6 and 9 are (6, 12, 18, 24, 30,…) and ( 9, 18, 27, 36,…) Correspondingly. There are 3 commonly used methods to find the LCM of 6 and 9 – by factoring primes, by division, and by listing the multiples. 1. LCM of 6 and 9 2. List of methods 3. Solved examples 4. Frequently asked questionsAnswer: LCM of 6 and 9 is 18. Read: What is LCM of 6 and 9 Explanation: Further reading: The LCM of two integers other than 0, x (6) and y (9), is the smallest positive integer m (18) that is divisible by both x (6) and y (9) without Methods to find The LCMs of 6 and 9 are explained below.
- According to the division method
- By multiples of the list
- According to the prime factorization method
LCM of 6 and 9 by Division Method
To calculate the LCM of 6 and 9 using the division method, we divide the numbers (6, 9) by their prime factors (preferably common). The product of these divisors for the LCM is 6 and 9.
- Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 6 and 9. Write this prime (2) to the left of the given numbers (6 and 9), separated by a ladder arrangement. .
- Step 2: If a given number (6, 9) is a multiple of 2 then divide it by 2 and write the quotient below. Bring down any number that is not divisible by primes.
- Step 3: Continue the steps until there are only 1s left in the last row.
The LCM of 6 and 9 is the product of all the primes to the left, i.e. LCM (6, 9) by division = 2 × 3 × 3 = 18.
LCM of 6 and 9 in List Multiples
Read more: What a cockroach bite looks like To calculate the LCM of 6 and 9 by listing the common multiples we can follow the steps below:
- Step 1: List some multiples of 6 (6, 12, 18, 24, 30,…) and 9 (9, 18, 27, 36,…)
- Step 2: The common multiples from multiples of 6 and 9 are 18, 36 ,. . .
- Step 3: The least common multiple of 6 and 9 is 18.
∴ Least common multiple of 6 and 9 = 18.
LCM of 6 and 9 in prime factors
The prime factors of 6 and 9 are (2 × 3) = 21 × 31 and (3 × 3) = 32, respectively. The LCM of 6 and 9 can be obtained by multiplying the prime factors raised to their highest powers, i.e. 21 × 32 = 18. Therefore, the LCM of 6 and 9 in prime factors is 18.☛ Also check:Read more: Which book series is like the wheel of time
- LCM of 32 and 64 – 64
- LCM of 36, 60 and 72 – 360
- LCM of 15 and 40 – 120
- LCM of 15, 20 and 25 – 300
- LCM of 12 and 30 – 60
- LCM of 3, 5 and 11 – 165
- LCM of 10 and 15 – 30
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