Question

Expalin lcm of 70,90,40​

Answer 1

Ответ:

2520

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Answer 2

The Least Common Multiple (LCM) of a set of numbers is the smallest multiple that is evenly divisible by all of the numbers in that set.

To find the LCM of 70, 90, and 40, you can follow these steps:

Step 1: Find the prime factorization of each number.

• Prime factorization of 70: 70 = 2 * 5 * 7

• Prime factorization of 90: 90 = 2 * 3 * 3 * 5

• Prime factorization of 40: 40 = 2 * 2 * 2 * 5

Step 2: Take the highest power of each prime factor that appears in the factorization of any of the numbers. In other words, for each prime factor, select the maximum exponent it has across all three numbers.

• The prime factor 2 has the highest exponent of 3 in the factorization of 90.

• The prime factor 3 has the highest exponent of 2 in the factorization of 90.

• The prime factor 5 has the highest exponent of 1 in the factorization of 70.

• The prime factor 7 only appears in the factorization of 70.

Step 3: Multiply these highest powers of the prime factors together:

LCM = 2^3 * 3^2 * 5^1 * 7^1

Step 4: Calculate the product:

LCM = 8 * 9 * 5 * 7

LCM = 5040

So, the LCM of 70, 90, and 40 is 5040.