QuestionFind the LCM of 90 and 20. The LCM of 90 and 20 is $$.

Studdy Solution

STEP 1

Assumptions1. We are finding the least common multiple (LCM) of90 and20. . The LCM of two numbers is the smallest number that is a multiple of both numbers.

STEP 2

First, we need to find the prime factorization of each number. The prime factorization of a number is a list of prime numbers that, when multiplied together, give the original number.
For90, the prime factorization is $90 =2 \times^2 \times5$

STEP 3

For20, the prime factorization is $20 =2^2 \times5$

STEP 4

To find the LCM of two numbers, we take each prime number that appears in either factorization, and raise it to the highest power that appears in either factorization.
In this case, the prime numbers are2,3, and.The highest power of2 that appears in either factorization is2 (from20's factorization), the highest power of3 is2 (from90's factorization), and the highest power of is1 (from either90 or20's factorization).

STEP 5

So, the LCM of90 and20 is $LCM(90,20) =2^2 \times3^2 \times5$

STEP 6

Now, we just need to calculate this expression to get the LCM.
$LCM(90,20) =2^2 \times3^2 \times5 =4 \times9 \times5$

STEP 7

Continue the calculation $LCM(90,20) =4 \times9 \times5 =36 \times5$

STEP 8

Finish the calculation $LCM(90,20) =36 \times5 =180$ So, the least common multiple of90 and20 is180.

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QuestionFind the LCM of 90 and 20. The LCM of 90 and 20 is $$.

Studdy Solution

STEP 1

Assumptions1. We are finding the least common multiple (LCM) of90 and20. . The LCM of two numbers is the smallest number that is a multiple of both numbers.

STEP 2

First, we need to find the prime factorization of each number. The prime factorization of a number is a list of prime numbers that, when multiplied together, give the original number.
For90, the prime factorization is $90 =2 \times^2 \times5$

STEP 3

For20, the prime factorization is $20 =2^2 \times5$

STEP 4

STEP 5

So, the LCM of90 and20 is $LCM(90,20) =2^2 \times3^2 \times5$

STEP 6

Now, we just need to calculate this expression to get the LCM.
$LCM(90,20) =2^2 \times3^2 \times5 =4 \times9 \times5$

STEP 7

Continue the calculation $LCM(90,20) =4 \times9 \times5 =36 \times5$

STEP 8

Finish the calculation $LCM(90,20) =36 \times5 =180$ So, the least common multiple of90 and20 is180.

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QuestionFind the LCM of 90 and 20. The LCM of 90 and 20 is $$.

Studdy Solution

STEP 1

Assumptions1. We are finding the least common multiple (LCM) of90 and20. . The LCM of two numbers is the smallest number that is a multiple of both numbers.

STEP 2

First, we need to find the prime factorization of each number. The prime factorization of a number is a list of prime numbers that, when multiplied together, give the original number.For90, the prime factorization is90=2×2×590 =2 \times^2 \times590=2×2×5

STEP 3

For20, the prime factorization is20=22×520 =2^2 \times520=22×5

STEP 4

STEP 5

So, the LCM of90 and20 isLCM(90,20)=22×32×5LCM(90,20) =2^2 \times3^2 \times5LCM(90,20)=22×32×5

STEP 6

Now, we just need to calculate this expression to get the LCM.LCM(90,20)=22×32×5=4×9×5LCM(90,20) =2^2 \times3^2 \times5 =4 \times9 \times5LCM(90,20)=22×32×5=4×9×5

STEP 7

Continue the calculationLCM(90,20)=4×9×5=36×5LCM(90,20) =4 \times9 \times5 =36 \times5LCM(90,20)=4×9×5=36×5

STEP 8

Finish the calculationLCM(90,20)=36×5=180LCM(90,20) =36 \times5 =180LCM(90,20)=36×5=180So, the least common multiple of90 and20 is180.

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First, we need to find the prime factorization of each number. The prime factorization of a number is a list of prime numbers that, when multiplied together, give the original number.
For90, the prime factorization is $90 =2 \times^2 \times5$

For20, the prime factorization is $20 =2^2 \times5$

So, the LCM of90 and20 is $LCM(90,20) =2^2 \times3^2 \times5$

Now, we just need to calculate this expression to get the LCM.
$LCM(90,20) =2^2 \times3^2 \times5 =4 \times9 \times5$

Continue the calculation $LCM(90,20) =4 \times9 \times5 =36 \times5$

Finish the calculation $LCM(90,20) =36 \times5 =180$ So, the least common multiple of90 and20 is180.