Question

Find the LCM of the following 12, 16, 36 ​

Answer 1

Answer:

LCM of 12, 16, 24, and 36 is 144.

Answer 2

Step-by-step explanation:

LCM of 12, 16, 24, and 36 is the smallest number among all common multiples of 12, 16, 24, and 36. The first few multiples of 12, 16, 24, and 36 are (12, 24, 36, 48, 60 .), (16, 32, 48, 64, 80 .), (24, 48, 72, 96, 120 .), and (36, 72, 108, 144, 180 .) respectively. There are 3 commonly used methods to find LCM of 12, 16, 24, 36 - by listing multiples, by prime factorization, and by division method.

The LCM of four non-zero integers, a(12), b(16), c(24), and d(36), is the smallest positive integer m(144) that is divisible by a(12), b(16), c(24), and d(36) without any remainder.

Let's look at the different methods for finding the LCM of 12, 16, 24, and 36.

By Prime Factorization Method

By Division Method

By Listing Multiples

LCM of 12, 16, 24, and 36 by Prime Factorization

Prime factorization of 12, 16, 24, and 36 is (2 × 2 × 3) = 22 × 31, (2 × 2 × 2 × 2) = 24, (2 × 2 × 2 × 3) = 23 × 31, and (2 × 2 × 3 × 3) = 22 × 32 respectively. LCM of 12, 16, 24, and 36 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 24 × 32 = 144.

Hence, the LCM of 12, 16, 24, and 36 by prime factorization is 144.

LCM of 12, 16, 24, and 36 by Division Method

To calculate the LCM of 12, 16, 24, and 36 by the division method, we will divide the numbers(12, 16, 24, 36) by their prime factors (preferably common). The product of these divisors gives the LCM of 12, 16, 24, and 36.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 12, 16, 24, and 36. Write this prime number(2) on the left of the given numbers(12, 16, 24, and 36), separated as per the ladder arrangement.

Step 2: If any of the given numbers (12, 16, 24, 36) is a multiple of 2, divide it by 2 and write the quotient below it. Bring down any number that is not divisible by the prime number.

Step 3: Continue the steps until only 1s are left in the last row.

The LCM of 12, 16, 24, and 36 is the product of all prime numbers on the left, i.e. LCM(12, 16, 24, 36) by division method = 2 × 2 × 2 × 2 × 3 × 3 = 144.

LCM of 12, 16, 24, and 36 by Listing Multiples

The value of LCM of 12, 16, 24, and 36 is the smallest common multiple of 12, 16, 24, and 36. The number satisfying the given condition is 144. ∴LCM(12, 16, 24, 36) = 144.

Hope its help..