Answered

Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Our platform connects you with professionals ready to provide precise answers to all your questions in various areas of expertise. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

the LCM of 400 and 600​

Sagot :

Multiples of 400: 400, 800, 1200, 1600
Multiples of 600: 600, 1200, 1800

So the LCM is 1200
reinhard10158

Step-by-step explanation:

the LCM (least common multiple) is the product (multiplication) of the longest product strings of the prime factors.

prime factors of a number start with 2 (the smallest prime number). we keep dividing the number (and then the results) by 2 until the division is not delivering a whole number anymore. then we switch to the next higher prime number. and so on, until the result is 1.

prime factors of 400

400 : 2 = 200

200 : 2 = 100

100 : 2 = 50

50 : 2 = 25

25 : 2 no

25 : 3 no

25 : 5 = 5

5 : 5 = 1

the prime factorization of 400 is therefore

2×2×2×2×5×5

prime factors of 600

600 : 2 = 300

300 : 2 = 150

150 : 2 = 75

75 : 2 no

75 : 3 = 25

25 : 3 no

25 : 5 = 5

5 : 5 = 1

the prime factorization of 600 is therefore

2×2×2×3×5×5

the LCM is now the product of the longest multiplication chains for the prime factors :

the longest chain for 2 is

2×2×2×2 in 400

for 3 is

3 in 600

for 5 is

5×5 in 400 and 600

the LCM = 2×2×2×2 × 3 × 5×5 = 1,200.

which is much smaller than the "instinctive" product of 400 and 600 :

400×600 = 240,000

which is of course also a multiple of 400 and 600, but not the smallest one (LCM).

We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.