Question

L.C.M of 144 and 200 using prime
factorisation method​

Answer 1

Answer:

lcm (144; 200) = 3,600: least common multiple, calculated. The numbers have common prime factors.

Step-by-step explanation:

Approach 1. Integer numbers prime factorization:

Approach 1. Integer numbers prime factorization:Prime Factorization of a number: finding the prime numbers that multiply together to make that number.

Approach 1. Integer numbers prime factorization:Prime Factorization of a number: finding the prime numbers that multiply together to make that number.144 = 24 × 32;

Approach 1. Integer numbers prime factorization:Prime Factorization of a number: finding the prime numbers that multiply together to make that number.144 = 24 × 32;144 is not a prime, is a composite number;

Approach 1. Integer numbers prime factorization:Prime Factorization of a number: finding the prime numbers that multiply together to make that number.144 = 24 × 32;144 is not a prime, is a composite number;200 = 23 × 52;

Approach 1. Integer numbers prime factorization:Prime Factorization of a number: finding the prime numbers that multiply together to make that number.144 = 24 × 32;144 is not a prime, is a composite number;200 = 23 × 52;200 is not a prime, is a composite number;

Approach 1. Integer numbers prime factorization:Prime Factorization of a number: finding the prime numbers that multiply together to make that number.144 = 24 × 32;144 is not a prime, is a composite number;200 = 23 × 52;200 is not a prime, is a composite number;* Positive integers that are only dividing by themselves and 1 are called prime numbers. A prime number has only two factors: 1 and itself.

Approach 1. Integer numbers prime factorization:Prime Factorization of a number: finding the prime numbers that multiply together to make that number.144 = 24 × 32;144 is not a prime, is a composite number;200 = 23 × 52;200 is not a prime, is a composite number;* Positive integers that are only dividing by themselves and 1 are called prime numbers. A prime number has only two factors: 1 and itself.* A composite number is a positive integer that has at least one factor (divisor) other than 1 and itself.

Approach 1. Integer numbers prime factorization:Prime Factorization of a number: finding the prime numbers that multiply together to make that number.144 = 24 × 32;144 is not a prime, is a composite number;200 = 23 × 52;200 is not a prime, is a composite number;* Positive integers that are only dividing by themselves and 1 are called prime numbers. A prime number has only two factors: 1 and itself.* A composite number is a positive integer that has at least one factor (divisor) other than 1 and itself.>> Integer numbers prime factorizat ion

ionCalculate the least common multiple, lcm:

ionCalculate the least common multiple, lcm:Multiply all the prime factors, by the largest exponents (if any).

ionCalculate the least common multiple, lcm:Multiply all the prime factors, by the largest exponents (if any).lcm (144; 200) = 24 × 32 × 52;

ionCalculate the least common multiple, lcm:Multiply all the prime factors, by the largest exponents (if any).lcm (144; 200) = 24 × 32 × 52;lcm (144; 200) = 24 × 32 × 52 = 3,600

ionCalculate the least common multiple, lcm:Multiply all the prime factors, by the largest exponents (if any).lcm (144; 200) = 24 × 32 × 52;lcm (144; 200) = 24 × 32 × 52 = 3,600the numbers have common prime factors

Answer 2

The given question is we have to find the LCM of

144 and 200.

Here, we have to use the prime factorisation method.

let us apply the prime factorisation method for the digit 144

$2)144 \\ 2)72 \\ 2)36 \\ 2)18 \\ 3)9 \\ 3)3$

The prime factors of the number 144 are 2*2*2*2*3*3

The exponential term in form of power is

${2 }^{4} \times {3}^{2}$

let's apply prime factorisation for the digit 200 we get

$2)200 \\ 2)100 \\ 2)50 \\2)25 \\ 5)25 \\ 5$

The factors of the number 200 are 2*2*2*2*5*5

The exponential form is

${2}^{4} \times {5}^{2}$

The LCM stands for the least common multiplier, where the LCM of two integers will divide the LCM of those two integers.

Therefore, the LCM of these two numbers will be

${2}^{4} \times {3}^{2} \times {5}^{2}$

The LCM will be 2*2*2*2*3*3*5*5

The LCM of 144 and 200 is 3600.

Therefore, the final answer to the given question is 3600.

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