Question

Lcm of 12 and 19 I will make ​

Answer 1

Answer:

please mark me as brainlist

Answer 2

Step-by-step explanation:

LCM of 12 and 19 is the smallest number among all common multiples of 12 and 19. The first few multiples of 12 and 19 are (12, 24, 36, 48, 60, . . . ) and (19, 38, 57, 76, 95, . . . ) respectively. There are 3 commonly used methods to find LCM of 12 and 19 - by division method, by listing multiples, and by prime factorization.

What is the LCM of 12 and 19?

Answer: LCM of 12 and 19 is 228.

LCM of 12 and 19

Explanation:

The LCM of two non-zero integers, x(12) and y(19), is the smallest positive integer m(228) that is divisible by both x(12) and y(19) without any remainder.

Methods to Find LCM of 12 and 19

The methods to find the LCM of 12 and 19 are explained below.

By Listing Multiples

By Division Method

By Prime Factorization Method

LCM of 12 and 19 by Listing Multiples

To calculate the LCM of 12 and 19 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 12 (12, 24, 36, 48, 60, . . . ) and 19 (19, 38, 57, 76, 95, . . . . )

Step 2: The common multiples from the multiples of 12 and 19 are 228, 456, . . .

Step 3: The smallest common multiple of 12 and 19 is 228.

∴ The least common multiple of 12 and 19 = 228.

LCM of 12 and 19 by Division Method

LCM of 12 and 19 by Division Method

To calculate the LCM of 12 and 19 by the division method, we will divide the numbers(12, 19) by their prime factors (preferably common). The product of these divisors gives the LCM of 12 and 19.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 12 and 19. Write this prime number(2) on the left of the given numbers(12 and 19), separated as per the ladder arrangement.

Step 2: If any of the given numbers (12, 19) 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 and 19 is the product of all prime numbers on the left, i.e. LCM(12, 19) by division method = 2 × 2 × 3 × 19 = 228.

LCM of 12 and 19 by Prime Factorization

Prime factorization of 12 and 19 is (2 × 2 × 3) = 22 × 31 and (19) = 191 respectively. LCM of 12 and 19 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 22 × 31 × 191 = 228.

Hence, the LCM of 12 and 19 by prime factorization is 228.

☛ Also Check:

LCM of 15 and 16 - 240

LCM of 148 and 185 - 740

LCM of 144 and 180 - 720

LCM of 144 and 169 - 24336

LCM of 14 and 91 - 182

LCM of 14 and 56 - 56

LCM of 14 and 49 - 98

Example 1: The GCD and LCM of two numbers are 1 and 228 respectively. If one number is 19, find the other number.

Solution:

Let the other number be m.

∵ GCD × LCM = 19 × m

⇒ m = (GCD × LCM)/19

⇒ m = (1 × 228)/19

⇒ m = 12

Therefore, the other number is 12.