MENU
❌
Home
Math Forum/Help
Problem Solver
Practice
Algebra
Geometry
Tests
College Math
History
Games
MAIN MENU
1 Grade
Adding and subtracting up to 10
Comparing numbers up to 10
Adding and subtracting up to 20
Addition and Subtraction within 10 or 20
2 Grade
Adding and Subtracting up to 100
Addition and Subtraction within 10 or 20
3 Grade
Addition and Subtraction up to 1000
Multiplication up to 5
Multiplication Table
Rounding
Dividing
Perimeter
4 Grade
Adding and Subtracting
Equivalent Fractions
Divisibility by 2, 3, 4, 5, 9
Area of Squares and Rectangles
Fractions
Equivalent Fractions
Least Common Multiple
Adding and Subtracting
Fraction Multiplication and Division
Operations
Mixed Numbers
Decimals
6 Grade
Percents
Signed Numbers
The Coordinate Plane
Equations
Polynomials
Symplifying Expressions
Polynomial Expressions
Factoring
7 Grade
Angles
Parametric Linear Equations
Word Problems
Exponentiation
Roots
Quadratic Equations
Vieta's Formulas
Progressions
Arithmetic Progressions
Geometric Progression
Progressions
Number Sequences
Reciprocal Equations
Logarithms
Logarithmic Expressions
Logarithmic Equations
Extremal value problems
Trigonometry
Geometry
Intercept Theorem
Law of Sines
Law of Cosines
Probability
Limits of Functions
Properties of Triangles
Pythagorean Theorem
Inverse Trigonometric Functions
Analytic Geometry
Easy
Normal
Difficult
Least Common Multiple - LCM - Problems with Solutions
Problem 1 sent by Maya
Find the least common multiple of 2 and 4.
Solution:
4 = 2 * 2.
4:2 = 2
4:4 = 1
So LCM of 2 and 4 is 4.
Problem 2
Find the least common multiple of 6 and 3.
Solution:
Since
6=3.2
, then
6|3
, so
LCM(6;3)=6
.
Problem 3
Find the least common multiple of 12 and 9.
Solution:
By definition, LCM(12;9) is the smallest number, which divides both 12 and 9. If we factorize them, we see that [tex]12=2^2.3[/tex] and [tex]9=3^2[/tex]. So, if
x
is the LCM of 12 and 9, then [tex]x|3^2[/tex],
x|3
and [tex]x|2^2[/tex].
x|3
follows from [tex]x|3^2[/tex], so we are left with [tex]x|3^2[/tex] and [tex]x|2^2[/tex]. Since [tex]3^2[/tex] and [tex]2^2[/tex] are coprime, [tex]x=2^2\cdot3^2=4\cdot9=36[/tex].
Problem 4
Determine the least common multiple of 7 and 3.
Solution:
Both 7 and 3 are prime, so they are also coprime. Then their LCM is their product, 21.
Problem 5
If
x
is the least common multiple of 8 and 9, find
x
.
Solution:
By factoring both numbers, we see that [tex]8=2^3[/tex], and that [tex]9=3^2[/tex]. They have no common prime factors, so they are coprime. Therefore their least common multiple is their product, 72.
Problem 6
Find the least common multiple of 7 and 12.
Solution:
We see that 7 is a prime number and is therefore coprime with any number, which is not divisible by 7. 7 does not divide 12, so 7 and 12 are coprime numbers. Therefore their LCM is their product, 84.
Problem 7
Find the least common multiple of
15
and
5
.
Solution:
Since
15=5 × 3
, the LCM of
15
and
5
is
15
.
Problem 8
Find the least common multiple of
4
and
10
.
Solution:
The first few multiples of 4 are 4,8,12,16,20,24,... and the first few multiples of 10 are 10,20,30,... The least number to appear in both sequences is 20, so it is the LCM of 4 and 10.
Problem 9
Find the least common multiple of 3 and 9.
Solution:
Since
9=3 × 3
, the LCM of 9 and 3 is 9.
Problem 10
Find the least common multiple of
15
and
6
.
Solution:
[tex]LCM(15;6)=LCM(3.5;3.2)=3.LCM(5;2)=3.5.2=30[/tex]
Problem 11
Find the least common multiple of
14
and
10
.
Solution:
[tex]LCM(14;10)=LCM(2.7;2.5)=2.LCM(7;5)=2.7.5=2.35=70[/tex]
Easy
Normal
Difficult
Submit a problem on this page.
Problem text:
Solution:
Answer:
Your name(if you would like to be published):
E-mail(you will be notified when the problem is published)
Notes
: use [tex][/tex] (as in the forum if you would like to use latex).
Correct:
Wrong:
Unsolved problems:
Contact email:
Follow us on
Twitter
Google+
Facebook
Author
Copyright © 2005 - 2018.