Answer :
To find the Lowest Common Multiple (L.C.M.) of two numbers, we typically follow these steps:
1. Identify the two numbers: Here, the two numbers are 24 and 42.
2. Find the Greatest Common Divisor (GCD) of the two numbers.
- The GCD of two numbers is the largest number that divides both of them without leaving a remainder.
- For our numbers, 24 and 42, the GCD is 6.
3. Use the relationship between GCD and L.C.M.:
- The formula to relate the GCD and L.C.M. of two numbers is:
[tex]\[ \text{L.C.M.} = \frac{\text{Product of the two numbers}}{\text{GCD}} \][/tex]
4. Calculate the product of the two numbers:
- Product of 24 and 42 is:
[tex]\[ 24 \times 42 = 1008 \][/tex]
5. Calculate the L.C.M. using the formula:
- Substitute the values of the product and the GCD into the formula:
[tex]\[ \text{L.C.M.} = \frac{1008}{6} = 168 \][/tex]
Thus, the Lowest Common Multiple (L.C.M.) of 24 and 42 is [tex]\(168\)[/tex].
1. Identify the two numbers: Here, the two numbers are 24 and 42.
2. Find the Greatest Common Divisor (GCD) of the two numbers.
- The GCD of two numbers is the largest number that divides both of them without leaving a remainder.
- For our numbers, 24 and 42, the GCD is 6.
3. Use the relationship between GCD and L.C.M.:
- The formula to relate the GCD and L.C.M. of two numbers is:
[tex]\[ \text{L.C.M.} = \frac{\text{Product of the two numbers}}{\text{GCD}} \][/tex]
4. Calculate the product of the two numbers:
- Product of 24 and 42 is:
[tex]\[ 24 \times 42 = 1008 \][/tex]
5. Calculate the L.C.M. using the formula:
- Substitute the values of the product and the GCD into the formula:
[tex]\[ \text{L.C.M.} = \frac{1008}{6} = 168 \][/tex]
Thus, the Lowest Common Multiple (L.C.M.) of 24 and 42 is [tex]\(168\)[/tex].
