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Answer:

It is the product of the two numbers.

Explanation:

The way to find the LCM is to write out both factorizations of the numbers, and then combine any factors that the two numbers share.

So, if two numbers don't share any factors greater than one, you won't combine anything, and so the LCM will just be all of the factors of the two numbers multiplied together.

Let's do an example so you can see what I mean:

Find the LCM of 7 and 15

The factorization of 7 is #7#. The factorization of 15 is #3 xx 5#.

Since none of these factors are the same, there is nothing to combine.

Therefore, the LCM is #3 xx 5 xx 7 = 105#

Answer:

#LCM=60#

Explanation:

When we're looking at the LCM (Least Common Multiple), we're looking for a number that both 12 and 15 are a factor of. Oftentimes people simply assume that if we multiply the two together, we'll find it. In this case, it'd be #12xx15=180#. 180 is a multiple of both, but is it the least one? Let's look.

I start with a prime factorization of both numbers:

#12=2xx2xx3#

#15=3xx5#

To find the LCM, we want to have all the prime factors from both numbers accounted for.

For instance, there are two 2s (in the 12). Let's put those in:

#LCM=2xx2xx...#

There is one 3 in both the 12 and the 15, so we need one 3:

#LCM=2xx2xx3xx...#

And there is one 5 (in the 15) so let's put that in:

#LCM=2xx2xx3xx5=60#

#12xx5=60#
#15xx3=60#

Answer:

#1%rarr1/100#

Explanation:

#1%#mean 1 out of #100#

so as a common fraction

#1%rarr1/100#

Answer:

0.035, 0.35, 3.5, 35.1

Explanation:

Given the numbers, 35.1, 3.5, .035, .35, write them in order from smallest to largest.

This can be done without any work, but it is a little easier to see the relative sizes, if the numbers are written with the same number of digits, or, at least, the same number of decimal digits.

There are 3 decimal digits in one of the numbers, so use that as a guide. Putting a zero in front of any "bare" decimals will also help.

Display with an equal number of digits:
# 35.100 #
# 03.500 #
# 00.035 #
# 00.350 #

Smallest to largest:
# 00.035 #
# 00.350 #
# 03.500 #
# 35.100 #

Now, we can remove the extra digits, but leave a zero in front of the decimals where there are.
# 0.035 #
# 0.35 #
# 3.5 #
# 35.1 #

Answer:

#2xx2xx2xx5xx5xx7#

Explanation:

To find the prime factorization of #1400#, we need to break it down into prime factors.

Lets use these steps I found in here: https://www.wikihow.com/Find-Prime-Factorization Follow along!

Step 1: Understand factorization. Hopefully you do, but just in case I'll explain.

  • Factorization: the process of breaking a larger number into smaller numbers (algebraic definition)

Step 2: Know prime numbers. They are basically numbers that can only be factored by 1 and itself. e.g. 5 (#5xx1#), 47 (#47xx1#)

Step 3: Start with the number, which is #1400#. It is always helpful to rewrite the problem, for it is easy to make mistakes if you don't.

Step 4: Start by factoring the number into any two factors.

  • #1400#: #200xx7#

Step 5: If the factorization continues, start a factorization tree, so it is less vulnerable to mistakes.
- #1400#
-tttt^
- #200# #7#

Step 6: Continue factorization.

  • #1400#
  • tttt^
  • #200# #7#
  • ttt^
  • #100# #2#
  • ttt^
  • #50# #2#
  • ttt^
  • #25# #2#
  • t^
  • #5# #5#

Step 7: Note any Prime numbers.

  • #1400#
  • tttt^
  • #200# #color(red)7#
  • ttt^
  • #100# #color(red)2#
  • ttt^
  • #50# #color(red)2#
  • ttt^
  • #25# #color(red)2#
  • t^
  • #color(red)5# #color(red)5#

Step 8: Finish factorization. I already did this in the #6th# step, so...

Step 9: Finish by writing the line of prime factors neatly in increasing order.

  • #color(blue)(1400: 2xx2xx2xx5xx5xx7)#
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