what is the least common multiple of 12 and 18
LCM of 12 and 18LCM of 12 and 18 is the smallest of all common multiples of 12 and 18. The first multiples of 12 and 18 are (12, 24, 36, 48, 60, 72, 84,.. ) and (18, 36, 54, 72,…) respectively. There are 3 commonly used methods to find the LCM of 12 and 18 – by enumerating the multiples, by prime factors and by division. 1. LCM of 12 and 18 2. List of methods 3. Solved examples 4. Frequently asked questionsAnswer: The LCM of 12 and 18 is 36. Read: what is the most common multiple of 12 and 18 Explanation: Read more: Use those extra mouse buttons to increase efficiency | The LCM of two integers other than 0, x (12) and y (18), is the smallest positive integer m (36) that is divisible by both x (12) and y (18) without a remainder. different methods to find the LCM of 12 and 18.
- According to the division method
- According to the prime factorization method
- By multiples of the list
LCM of 12 and 18 by Division Method
To calculate the LCM of 12 and 18 using the division method, we divide the numbers (12, 18) by their prime factors (preferably regular). The product of these divisors for the LCM is 12 and 18.
- Step 1: Find the smallest prime that is a factor of at least one of the numbers, 12 and 18. Write this prime (2) to the left of the given numbers (12 and 18), separated by a ladder arrangement. .
- Step 2: If a given number (12, 18) 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 12 and 18 is the product of all the primes to the left, i.e. LCM (12, 18) by division = 2 × 2 × 3 × 3 = 36.
LCM of 12 and 18 in prime factors
Read more: what is the ph of milk of magnesia | The initial Q & APrime balances of 12 and 18 are (2 × 2 × 3) = 22 × 31 and (2 × 3 × 3) = 21 × 32. The LCMs of 12 and 18 can be obtained by multiplying, respectively. prime factors are raised to their highest powers, i.e. 22 × 32 = 36. Therefore, the LCM of 12 and 18 in prime factors is 36.
LCM of 12 and 18 in List Multiples
To calculate the LCM of 12 and 18 by enumerating common multiples, we can follow these steps:
- Step 1: List some multiples of 12 (12, 24, 36, 48, 60, 72, 84,…) and 18 (18, 36, 54, 72,…)
- Step 2: The common multiples from multiples of 12 and 18 are 36, 72 ,. . .
- Step 3: The least common multiple of 12 and 18 is 36.
∴ Least common multiple of 12 and 18 = 36.☛ Also check:Read more: Can I Use Base Paint Without Color? | Top Q&A
- LCM of 15 and 27 – 135
- LCM of 15 and 25 – 75
- LCM of 15 and 24 – 120
- LCM of 15 and 21 – 105
- LCM of 15 and 20 – 60
- LCM of 15 and 18 – 90
- LCM of 15 and 17 – 255
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